# Questions on Geometry: Points, lines, angles, perimeter answered by real tutors!

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 Geometry: Points, lines, angles, perimeter Solvers Lessons Answers archive Quiz In Depth

Question 751253: Which equation represents a line perpendicular to the line whose equation is 2x+3y equals 12?
(1) 6y equals -4x+12 (3) 2y equals -3x+6
(2) 2y equals 3x+6 (4) 3y equals -2x+12
Please show me how you did it. Thank You

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Sort the equation into y = mx + c
2x + 3y = 12 => 3y = -2x + 12 => y = -2/3x + 4.
This equation has a gradient = -2/3
For a line to be perpendicular to another,
their gradients multiply together to = -1
So if this equation's gradient = -2/3
then the other line's gradient = 3/2
-2/3 * 3/2 = -1
Check the gradients from (1) - (4)
1) -4/6 = -2/3
2) 3/2
3) -3/2
4) -2/3
Hope this helps.
:-)

Question 750024: Rectangle QRST between curve and . Let P be the point of intersection of the side QT and the x-axis. Let α be the length of the perimeter of this rectangle. We are to find the x-coordinate of the point P where α is maximized and also to find the maximum value of α. P(x,0), where 0 Therefore, when x=(A), α is maximized and its maximum value is (B)
solve for A and B
((this is the picture of the graph http://i44.tinypic.com/30sk9ir.jpg)

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Both curves and the rectangle QRST are symmetrical with respect to the y-axis.
TI'll call the coordinates of P (a,0), to distinguish that x-coordinate value from the variable .
The x-coordinates of points R and S are the same .
The y-coordinate of points Q and R, on curve is .
The y-coordinate of points S and T, on curve is .
The width ST (or QR) of the rectangle is .
The height RS (or QT) of the rectangle is .
The perimeter of the rectangle is

It's maximum is at
because a parabola such as has a vertex as
The equation in vertex form would be

So the maximum value of happens at
and the maximum value of is

Question 749485: rectangel QRST, side QR is parallel to x-axis and on y>0 of the quadratic funtion . And the side ST on the y<0 of the quadratic function . Let P be the point of intersection of the side QT and the x-axis. Let α be the length of the perimeter of this rectangle. We are to find the x-coordinate of the point P where α is maximized and also to find the maximum value of α. P(x,0)

Question 749242: WHAT ARE THE POINTS FOR x-2y=-4???
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The set of points whose coordinates satisfy the given equation has infinite elements. You can find as many as you like by choosing values to substitute for and then doing the arithmetic to determine the value of that results. Other than that, I have no idea what you are talking about. By the way, one question mark is sufficient to indicate that you are asking a question.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 747774: Here is my question I need to answer:
Draw 2 line segments AB and CD that:
A. Intersect, but neither segment bisects the other
B. Intersect, with each bisecting the other
C. Intersect, with AB bisecting CD, but not vice versa
I have drawn my line AB going straight across, I then drew line CD going up and down off to the right side of line AB. Now I am completely lost with what to do.

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We are given
Here is my question I need to answer:
Draw 2 line segments AB and CD that:
A. Intersect, but neither segment bisects the other
B. Intersect, with each bisecting the other
C. Intersect, with AB bisecting CD, but not vice versa

The key to answering this problem is that LINE SEGMENTS have a specific length
so when you answer B) both line segments have the same length and with C) they are of different length

Question 744724: Graph the equation x+3=y by finding three points on the line
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Substitute x values into your equation to obtain the y coordinate.
x= -2 => -2 + 3 = 1 : y = 1
x = 0 => 0 + 3 = 3 : y = 3
x = 2 => 2 + 3 = 5 : y = 5
So your 3 points on this line are:
(-2, 1) (0, 3) and (2, 5)

Question 742555: For a 67^0:
A. What is the measure of its supplement?
B. What is the measure of its complement?

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67^0=1
A) 179 degrees
B) 89 degrees

Question 741579: Indicate in standard form the equation of the line passing through the given points.
L(5, 0), M(0, 5)

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Indicate in standard form the equation of the line passing through the given points.
L(5,0), M(0,5)
----------
x + y = 5

Question 741576: Indicate in standard form the equation of the line passing through the given points.
P(6, 2), Q(8, -4)

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slope

Pick either point and use the ordered pair values in slope-intercept form of equation:
Picking P(6,2),
, general way to show slope intercept form of line equation.
, where b is the y-intercept.

You want equation in standard form, but we can more quickly write the slope-intercept form. Not a problem. We can convert into standard form:

, just by adding +3x to both sides. In other examples, sometimes a couple more steps are needed.

Question 741363: Can you help me solve this problem it is slope intercept form (0,0) m= -2 ?
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 Solved by pluggable solver: FIND a line by slope and one point What we know about the line whose equation we are trying to find out: it goes through point (0, 0) it has a slope of -2 First, let's draw a diagram of the coordinate system with point (0, 0) plotted with a little blue dot: Write this down: the formula for the equation, given point and intercept a, is (see a paragraph below explaining why this formula is correct) Given that a=-2, and , we have the equation of the line: Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . Here's the graph:

Question 739899: Sorry if not in the right category:
One room is 12ftx16ft and the other room is 10ftx20ft
If tile costs $3.00 per square foot, ans labor for installation costs$2.00 per square foot, how much will it cost to tile the two rooms?

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One room is 12ftx16ft and the other room is 10ftx20ft
If tile costs $3.00 per square foot, ans labor for installation costs$2.00 per square foot, how much will it cost to tile the two rooms?
----------------
Tile + labor = \$5/sq ft
---
Area = 12*16 + 10*20 sq ft

Question 737131: Identify the min/max point for the expression: y=(2x-6)(x-7)
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The extreme point is right between the zeros. the leading term when you multiply to put into general form ( although you don't really need this in general form) is 2x^2, so the parabola will have a minimum.

The zeros will be when 2x-6=0 and when x-7=0. Find that middle value, plug it into the function, and that's you minimum y value.

Question 735925: Find an equation of the line that has a y intercept of -1 that is parallel to the graph of the line x-3y=6.
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Immediately seen is , and we want the same slope as in , which is , so you are looking for .

Question 733766: Write the equation for the vertical line that contains point E(10,-3).
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( 10,-3)
For every point on the line, ,
so that is the equation of the line

Question 733680: Find the distance between each pair of points.
a. (2,15) and (-3,4)
b. (-9,0) and (3,-10)

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(A)√146≈12.0830
(B)2√61≈15.6205

Question 733511: what is the line in standard from that passes through (6,-7)(6,6)?

Question 733475: ok their is a triangle one of the angles measures is 7x+10. another measure is 2x. the thired measure is x+20 what is the measure of the largest angle?
Found 2 solutions by solver91311, josgarithmetic:
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The sum of the measures of the interior angles of any triangle is . So:

Solve for . Then calculate

You wrote "their [sic] is a triangle. . ."

Is English class your nap time?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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The sum of the measures of the triangle's interior angles is 180 degrees. You have expressions for the three angles and each is an expression with the only variable x. What can you do with this?

Question 733096: Based on the this problem, can you approximate a line of best fit by writing an equation? Use t for packing time and s for the number of shipments packed.
The original question is: The table shows the relationship between the number of shipments packed and the time spent packing for a group of workers at a mail order company.
Minutes spent packing: 30 45 60 75 90
Shipments packets: 244 342 490 619 705
Plot the date points: This has been answered in the graph provided.
b. Are there any points that Outliers? If so, what possible explanation could there be for the existence of this discrepancy from the other data?

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The original question is: The table shows the relationship between the number of shipments packed and the time spent packing for a group of workers at a mail order company.
Minutes spent packing: 30 45 60 75 90
Shipments packets: 244 342 490 619 705
Plot the date points: This has been answered in the graph provided.
-----
I plotted the points and found the least squares regression equation.
#of packets(t) = 7.99t + 0.4
----
p(2) = 7.99*2 + 0.4 = 16.38 packets
------------------------------------------
b. Are there any points that Outliers?
Ans: No
--------
If so, what possible explanation could there be for the existence of this discrepancy from the other data?
Ans: Erroneous data entry.
==============================
Cheers,
Stan H.
============================

Question 732663: AOB and COD are two perpendicular diameters of a circle with radius 4 feet. With center A and radius AB an arc is drawn from B to meet AC extended at P, and with center B and radius BA an arc is drawn from A to meet BC extended at Q. With center C the arc PQ is drawn. DC extended meets this arc at R. Find DR and the perimeter of ADBPRQ.
So far, line segment AO, OC, OB, and OD are all 4 feet. Triangle ACO and OCB are 45-45-90. Line segments AC and CB are 3 root 2. Angles QCR and RCP are each 45 degrees, making arc QP 90 degrees. I really don't know where to go from here. Can someone please help? I have been stuck on this for days!

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I did not know how to draw just the arc PQR, so I had to draw the whole green circle.
The sides of the square ADBC are in length.
because they are radii of the circles containing the arcs BP and AQ
so all radii of my green circle containing arc PRQ

So

BPA and QAB are isosceles triangles with a vertex angle and legs measuring 8 feet.
Based on law of cosines or using the fact that BPC and AQC are right triangles, we can calculate that
The approximate length would be
Otherwise we could split those triangles into two congruent right triangles with a angle and 8-foot hypotenuse, and calculate the length of their short legs (in feet) as
Either way the ratio of base to leg length in those isosceles triangles is

PRC and RQC are also isosceles triangles with a vertex angle, so they are similar to BPC and AQC.
We knew that the length of their legs (in feet) were
and multiplying that times the ratio found above for the similar triangles we can find the length of .
Giving up on accurate value expressions,
,
so

Now we can calculate the perimeter of ADBPRQ as the approximate value (in feet) of

Question 732089: AOB and COD are two perpendicular diameters of a circle with radius 4 feet. With center A and radius AB an arc is drawn from B to meet AC extended at P, and with center B and radius BA an arc is drawn from A to meet BC extended at Q. With center C the arc PQ is drawn. DC extended meets this arc at R. Find DR and the perimeter of ADBPRQ.

So far, line segment AO, OC, OB, and OD are all 4 feet. Triangle ACO and OCB are 45-45-90. Line segments AC and CB are 3 root 2. Angles QCR and RCP are each 45 degrees, making arc QP 90 degrees. I really don't know where to go from here. Any ideas?

Question 731833: angles a and b are supplementary . What is meseaurement of angle b if measeaurement of angle a =120 degrees

Question 731527: find the equation of a line passing through the point (5, 3) and parallel to the line y=-3
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Any line parallel to y = -3 will be of the form y = k, where k is any number.

In this case, k has to be 3 since y = 3 goes through the point (5,3). Basically all points on the line y = 3 have a y coordinate of 3.

So the answer is y = 3

Question 731245: A line parallel to y=2/3x-7 is
You can put this solution on YOUR website!
A line parallel to y=2/3x-7 is
-----
Parallel to the line.

Question 725621: Find the interior angles of the triangle with the given vertices (1,2) (3,4) (2,5)
Answer by Edwin McCravy(8908)   (Show Source):
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Find the interior angles of the triangle with the given vertices (1,2) (3,4) (2,5)
You can do this two different ways.

Method 1:
A. Use the distance formula to find the length of the three sides.
B. Use then law of cosines.

Method 2:
1. Find the slopes of the three sides.
2. Use the tangent formula for the angles between two sides.

Method 2 is easier.

Let's draw the triangle and extend the sides:

(1,2) (3,4) (2,5)

We  use the slope formula, which is

m =

three times to find these three slopes:

the slope of the green line is m = 1
the slope of the red line is m = 3
the slope of the blue line is m = -1

Here is the formula for the acute angle between two lines, one with
slope m1  and the other with slope m2.

with each pair of lines.  Except when two lines are perpendicular
there are TWO angles between any pair of lines, an acute angle and an
obtuse angle which are supplementary.

If the denominator of that fraction
comes out 0, making it undefined, that means the angle between
the two lines are perpendicular and the angle between them is 90°.

I'll just find the angle between the green and red lines. You find
the others:

Using the inverse tangent function on a calculator, we get

q = 26.56505118°.

That's the acute angle between the green and red lines.
The obtuse angle between them is 180°-26.56505118° or 153.4349488°

The acute angle between the red and blue lines is 63.43494882°
The obtuse angle between them is 180°-63.43494882° or 116.5650512°.

The angle between the green and blue line is 90°.  (You can also
tell that because their slopes are negative reciprocals 1 and -1.)

Since it is a right triangle the other two angles besides the
right angle are acute angles.

Edwin

Question 725604: Answer each of the following T (true) or F (false). If FALSE, provide a counterexample (a figure that proves the statement is false).
True._____ (a) The diagonals of a square are perpendicular to each other.
False .______ (b) If all sides of a quadrilateral are congruent, the quadrilateral is a rhombus.
___False .____ (c) The diagonals of a parallelogram are congruent.
___False .____ (d) The diagonals of a kite are perpendicular to each other.
__False ._____ (e) The diagonals of a rectangle bisect the opposite angles.
___True.____ (f) The opposite angles of a rhombus are congruent.

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There you go ,

Question 725475: If the perimeter of the triange is 32 inches, what is the length of the longest side if there are two equal sides and a third side that is five inches more than the length of the two equal sides?
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x+x+x+5=32
3x=27
x=27/9
x=9
x+5=14 long side

Question 725229: What is the equivalent standard form equation for this line?
3y = 6x + 9

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3y = 6x + 9

-6x + 3y = 9

6x - 3y = -9

Answer: 6x - 3y = -9

Question 721573: a gardner is fencing off a rectangular area area with a fixed perimeter of 68 feet. What is the maximum area?
A) 1156 ft2
B) 17 ft2
C) 289 ft2
D) 4.25 ft2
E) None

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Easy to answer with only a little bit of thinking and without writing anything (except for squaring a number in your head).
Cut the 68 into four equal parts and then square the result.

A more analytical way to solve:

The perimeter is already set at 68 feet. The question asks, what is the largest area for this rectangular region, based on that given perimeter. Using x and y for length and width, we have these:

and . A is for AREA. Using the perimeter equation,

Substituting this into A equation,

, which shows that A has a maximum, which would be at the vertex of the graph of A.

Find the vertex! Put A(x) into standard form, and read the vertex point from standard form equation function A(x).

Vertex is at (17,289). This will obviously be a SQUARE SHAPE. 17+17+17+17=68.
Note that a rectangle has its maximum area when it is a square. This is why one could solve this problem almost entirely in ones head.

Question 720849: the ratoio of the supplementary angle and the complementary angle of an angle is 8:3 .find the angle

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If you have two unknown numbers but you know what they add up to, then a single variable can be used to express both unknowns. For example, if two unknown numbers add up to 100, then use "x" for one number. The other number will be (100-x). This is a good thing to know when solving word problems. The fewer variables you use, the easier the solution will be.

We can use this in solving your problem. Supplementary angles are two angles that add up to 180 degrees. So if "an angle" is "x", then the supplementary angle would be (180-x). Complementary angles are two angles that add up to 90 degrees. So if "an angle" is still "x", then the complementary angle would be (90-x).

We are told that the ratio of these the supplementary and complementary angles is 8:3. So:

Since we used just one variable, we can solve the problem with this one equation. (If we had used two variables we would need two equations. If we had used three variables we would need three equations.) Our equation is a proportion (one fraction equals another fraction) so we can use cross-multiplying:

Simplifying...

Subtracting 540:

Dividing by 5:

Since "x" was "an angle" it is the angle we were asked to find. (If we were asked to find the supplementary angle we would find 180 - x = 180 - 36 = 144. If we were asked to find the complementary angle we would find 90 - x = 90 - 36 = 54.)

Question 720732: Perform the following operations. Leave your answers in simplest form.
a. 21 degrees 35' 31" + 49 degrees 51' 32"
b. 93 degrees 38' 14" - 13 degrees 49' 27"
Express the following in degrees, minutes and seconds without decimals:
a. 10.3 degrees
b. 15.14 degrees

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recall that degree=', and '="
a. degrees ' " + degrees ' "...add degrees and degrees, min and min, sec and sec
( degrees+ degrees)+ (' + ')+("+")

degrees ' "....note that you have ' and it is equal to degree and '...so; add degree to degrees
degrees '"....note that you have " and it is equal to ' and "..so; add ' to min
degrees '"

b. degrees ' " - degrees ' "
subtract degrees from degrees, min from min, sec from sec
degrees ' "
degrees ' " ...as you can see, you cannot subtract ', so you borrow degree from degrees and convert it in min and add to '
degrees ' "
degrees ' "....you cannot subtract ", so you borrow ' convert it in sec and add to "

degrees ' "

degrees ' "

Express the following in degrees, minutes and seconds without decimals:
a. degrees = degrees' = degrees'
b. degrees
= degrees'
= degrees'
= degrees'"
= degrees'"

Question 720570: Find the slope of the line through the points P1 ?(-2/3, 1/2) and P2 (3/4, 7/8)
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x1 y1 x2 y2
- 2/ 3 1/ 2 3/ 4 7/8

slope m = (y2-y1)/(x2-x1)
( 7/8 - 1/2 )/( 3/4 - - 2/3 )
( 3/8 / 1.42 )
m= 1/4

Question 719828: a transversal cuts two parallel lines. <1 and <2 are two interior angles on the same side of the transversal. find the measures of <1 and <2 if <1=2x - 25 and <2 = x + 88
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The sum of the measures of two interior angles on the same side of a transversal is 180. So:

Solve for , then calculate and

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 719739: The y- intercepts of the equation 3x – 4y = 12 is the point.
You can put this solution on YOUR website!
The y- intercepts of the equation 3x – 4y = 12 is the point.
-------------
Thx for letting us know.

Question 719617: Determine whether ABCD is a rectangle by using the given set of vertices. Quadrilateral ABCD has vertices with coordinates A (4,1), B (5,3), C (7,3), and D (6,1). NOW use the calculated slopes of the adjacent sides to determine whether ABCD is a rectangle. Is ABCD a rectangle?

Question 719618: Determine whether ABCD is a rectangle by using the given set of vertices. Quadrilateral ABCD has vertices with coordinates A (4,1), B (5,3), C (7,3), and D (6,1). NOW use the calculated slopes of the adjacent sides to determine whether ABCD is a rectangle. Is ABCD a rectangle?

Question 719616: Determine whether ABCD is a rectangle by using the given set of vertices. Quadrilateral ABCD has vertices with coordinates A (4,1), B (5,3), C (7,3), and D (6,1). FIRST find the slopes of the pairs of opposite sides to first determine whether ABCD is a parallelogram. Is ABCD a parallelogram?

Question 719615: Determine whether ABCD is a rectangle by using the given set of vertices. Quadrilateral ABCD has vertices with coordinates A (4,1), B (5,3), C (7,3), and D (6,1). FIRST find the slopes of the pairs of opposite sides to first determine whether ABCD is a parallelogram. Is ABCD a parallelogram?

Question 717256: a window had a length of 110 feet and width of 120. what is the area of the window
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ft
ft
ft2
ft2
ft2

Question 716817: Angles 1 and 2 are a linear pair, the measure of angle 1=x-39, and the measure of angle 2=x+61. Find the measure of each angle.
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Angles 1 and 2 are a linear pair, the measure of angle 1=x-39, and the measure of angle 2=x+61. Find the measure of each angle.
------
Equation:
x-39 + x+61 = 180
2x + 22 = 180
x + 11 = 90
x = 79
---
Ans: x-39 = 40 degrees
x+61 = 140 degrees
============================
Cheers,
Stan H.
================

Question 714818: Indicate the equation of the given line in standard form. The line with slope 9/7 and containing the midpoint of the segment whose end points are (2, -3) and (-6, 5).
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the midpoint of the segment whose end points are (2, -3) and (-6, 5)
is [(2-6)/2,(-3+5)/2]=(-2,1)
the equation of the line in standard form with slope 9/7 and containing (-2,1)
is (y-1)/(x+2)=9/7
or 7(y-1)=9(x+2)
or 7y-7=9x+18
or 7y-9x-25=0

Question 713924: A line passes through the points (-10, -4) and (-1,2). What is the y-intercept of the line?
a) (-4,0)
b) (0, -4)
c) (8/3, 0)
d) (0, 8/3)

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Use the two given points to find the line, in any form.
Trying formula for slope, m=(2--4)/(-1--10), m=6/9, m=2/3.
Try now point-slope form. y-2=(2/3)(x-(-1)),

Convert the equation to slope intercept form.
y-2=(2/3)(x+1)
y=(2/3)x+2/3+2

Read the value for the y intercept directly from the equation.
y=mx+b common general formula for slope-intercept form equation for a line, so b=?
.....

Question 710926: Find the slope of the line that contains the points (–11,11) and (–1,–7).
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slope of the line that contains the points (–11,11) and (–1,–7).
-----
slope = (11--7)/(-11--1) = 18/-10 = -9/5
=================
Cheers,
Stan H.
=================

Question 710806: How do I get an equation to a point slope form that passes through (-4,6) and (-2,5)