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

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Question 994003: If angle T=angle S.PT=RS and PT//RS,Then PTRS is a???
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PTRS is a Parallelogram. Opposite angels are equal(angel T= angel S)) and two of the opposite sides are parallel and equal(PT=RS and PT//RS).

Question 993746: which of these angles are supplementary?
• Vertical
•Linear
• Corresponding
• Alternate Interior
• Alternate Exterior
•Same Side Interior

Question 993181: <2 and <10 are what kind of angles?

Question 992488: what are the coordinates of the midpoint of the line segment with endpoints (2 -5) and (8 3)
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Follow the formula for finding midpoint of two given points!

(5,-1)

Question 992135: a, b, and c are points in the number line. a = -9, b = 21, and c = 7. If c is between a and b, find the ratio ac:cb.
Found 2 solutions by MathTherapy, ikleyn:
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a, b, and c are points in the number line. a = -9, b = 21, and c = 7. If c is between a and b, find the ratio ac:cb.
Too much info.
ac = 7 - - 9, or 16
cb = 21 - 7, or 14
= , or



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.
a, b, and c are points in the number line. a = -9, b = 21, and c = 7. If c is between a and b, find the ratio ac:cb.
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1.  These words are excessive:  "If c is between a and b".
It follows the condition  "a = -9, b = 21, and c = 7".

2.  ac = 9 + 7 = 16.
cb = 21 - 7 = 14.

Therefore   ac:cb = = = .

(ac  and  cb are the length of the corresponding segments).

Question 992001: I'm thinking this should be an easy assignment, but I'm getting a mental block. The following is the assignment:
Write a conjecture based on the given information.
A, B, C, and D are coplanar points.

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ABCD is a quadrilateral, a triangle, or a line depending on whether the maximum number of collinear points is 2, 3, or 4

John

My calculator said it, I believe it, that settles it

Question 991976: how do you graph y=-5/3x+2
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.
Is the equation:

.
Or:

.
Or:

.
Use parentheses to clarify and re-post your question.

Question 991719: If m abc = 7x - 3 and m cbd = 2x + 12 then find x
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You need to describe the two angles.
Cheers,
Stan H.
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Question 991489: Suppose Q is a point on RW. IF QW = 12, what are, what are the possible coordinates of Q?
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You have not provided enough information to solve the problem.
Is there a diagram?

Question 991475: What are the coordinates of point C such that it is the point that is a ratio of 1/5 of the distance between A(8,-8) and B(-7,-3)
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What are the coordinates of point C such that it is the point that is a ratio of 1/5 of the distance between A(8,-8) and B(-7,-3)
----
x-change in AB:: -15
y-change in AB:: 5
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Coordinates of C::
x coordinate:: 8+ (1/5)(-15) = 8-3 = 5
y coordinate:: -8 + (1/5)(5) = -8+1 = -7
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Ans: (5,-9)
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Cheers,
Stan H.

Question 989639: In the diagram below, X is the midpoint of line VZ, VW = 5, and VY = 20. Find the coordinates of W, X, and Y.
Picture of line and points: http://i.imgur.com/0WIjt86.jpg

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X is the midpoint so,

.
.
.

.
.
.

Question 990464: -6(-5+4a) < -38-7a
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-6(-5+4a) < -38-7a

30 - 24a < -38 - 7a

Group like terms:
-24a + 7a < -38 - 30

= -17a < -68

Divide both sides by -17,

-17a/-17 < -68/-17

Since the left-side of the inequality is negative, change the direction of the sign,
a > 4

Question 990454: if two lines intersect then the intersection is a?
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.
. . . then the intersection is a point.

Question 989546: The midpoint of MN is point P at (–4, 6). If point M is at (8, –2), what are the coordinates of point N?
(–16, 14)
(–10, 5)
(2, 2)
(6, 2)

Found 2 solutions by josmiceli, solver91311:
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The x-coordinate of the midpoint is at:

where and are
x-coordinates of the endpoints
----------------------------------
The y-coordinate of the midpoint is at:

where and are
y-coordinates of the endpoints
----------------------------------
I will say that:
( x[1], y[1] ) = M( 8, -2 )
( x[p], y[p] ) = P( -4, 6 )
I need to find N( x[2], y[2] )
--------------------------
First, using:

--------------------
Next, using:

--------------------------------
The other endpoint is at: N( -16, 14 )
--------------------------------
check:

and

OK

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Use the midpoint formulas. Substitute your values for and then solve for and , the coordinates of the other endpoint.

and

John

My calculator said it, I believe it, that settles it

Question 989335: What is the distance between points K(-9,8) and L(-6,0)
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 Solved by pluggable solver: Distance Formula The first point is (x1,y1). The second point is (x2,y2) Since the first point is (-9, 8), we can say (x1, y1) = (-9, 8) So , Since the second point is (-6, 0), we can also say (x2, y2) = (-6, 0) So , Put this all together to get: , , , and -------------------------------------------------------------------------------------------- Now use the distance formula to find the distance between the two points (-9, 8) and (-6, 0) ========================================================== Answer: The distance between the two points (-9, 8) and (-6, 0) is exactly units The approximate distance between the two points is about 8.54400374531753 units So again, Exact Distance: units Approximate Distance: units

Question 989053: the length of the base of an isosceles triangle is one third the length of the equal sides .if the perimeter of the triangle is 28 cm long .how long is the base ? thank you so much could you pls help ?
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Hi dear,
Let k be the lenght of the base and m be the lenght of the equal sides.
k=m/3-----(1)
also,
2m+k=28---(2)
put 1 in 2,
2m+(m/3)=28
6m+m=84
7m=84
m=12
put m=12 in 1
k=12/3
k=4
From the above,
The lenght of the base is 4
and the equal sides is 12.
HOPE THIS HELPS?
::TIMNEWMAN::

Question 988707: Points R , S and T are collinear with point S in between points R and T . If mRS = x + 1 , mST = 5 cm and mRT = 18 cm find the valie of x and the measure of line segment RS.

Question 987710: Determine the equation of the line through A(-5,1) such that the distance from B(3, -1) and C(-3, 2) to that line is equal.
Thank you!

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Determine the equation of the line through A(-5,1) such that the distance from B(3, -1) and C(-3, 2) to that line is equal.
----------------
To be equidistant, the line has to go thru the midpoint of B & C
Find the midpoint.
Find the line thru A and the MP.

Question 987212: Find the coordinate points M(8,-), N (-,13), MN =square root of 113

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M(8,y), N(x,13), MN=sqrt(113).

The missing coordinate values are infinitely many; x depends on y or y depends on x.

Question 987199: On January 3rd 2004, after a journey of 300 million miles, the rover Spirit landed on Mars and began sending back information to earth. It landed only 6 miles from target. This accuracy is comparable to shooting an arrow at a target 50 feet away and missing the exact center by what distance?
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.
=0.000002%
=

Question 987023: S is the midpoint of rt, rs = -2× and st = -3×-2, find rs, st and rt
Found 2 solutions by stanbon, Boreal:
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S is the midpoint of rt, rs = -2× and st = -3×-2, find rs, st and rt
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Draw the picture::
R........S.......T
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rs = -2x
st = -3x-2
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Since S is the midpoint,
-2x = -3x-2
x = -2
-----
Ans:
rs = -2x = 4
st = -3x-2 = 4
rt = 8
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Cheers,
Stan H.
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-2x=-3x-2, since the two lengths are equal (midpoint)
x=-2
4=4; as it should be.
The lengths of rs and st are 4
The length of rt is 8.

Question 986609: This is about division of line segment.
Q: Line Segment AB where A(-4,-3) and B(7,1) is trisected. Find the points of trisection.
Thank you

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In the x direction, the distance from A to B is,

Divide that in 3 for 3 equal steps from A to B.

Similarly for the y direction,

So the two points are (,) and (,).
.
.
.

Question 986656: In my Geometry Book it says line GH has endpoints G(-3,2) and H(3,-2)
The question says find GH to the nearest tenth?

Found 3 solutions by josgarithmetic, mananth, stanbon:
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G and H form the hypotenuse of either of two right triangles. Look at the two points on a cartesian system. The third point may be either (-3,-2), or alternatively (3,2). Either choice, G, and H, and either of the third point form a RIGHT TRIANGLE. You can use Pythagorean Theorem formula to find length GH.

Taking the third point as T(-3,-2), your triangle has legs of lengths 4 and 6; look at the placements and coordinates of the points on your cartesian system for the plotted T, G, and H. The hypotenuse GH will be .

Look in your book if you want to see a derivation of the Distance Formula. It is essentially a form of the Pythagorean Theorem.

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G(-3,2) and H(3,-2)
(x1,y1) and (x2,y2)
distance formula

d=

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In my Geometry Book it says line GH has endpoints G(-3,2) and H(3,-2)
The question says find GH to the nearest tenth?
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Formula for distance:: D = sqrt[(change in x)^2+(change in y)^2]
-----
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D = sqrt[(3--3)^2 +(2--2)^2]
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D = sqrt[6^2 + 4^2]
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D = sqrt(36+16)
----
D = sqrt(52)
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D = sqrt(4*13)
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D = 2sqrt(13)
----------------
Cheers,
stan H.
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Question 986318: Two lines perpendicular to a plane are parallel to each other.
Sometimes always or never?

Found 2 solutions by Alan3354, stanbon:
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Two lines perpendicular to a plane are parallel to each other.
Sometimes always or never?
=======================
Always, if by perpendicular you mean normal.
================
PS 3 dimensions is a LOT more difficult (and more interesting) that 1.5 time 2 dimensions.

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Two lines perpendicular to a plane are parallel to each other.
Sometimes always or never?
-------
Ans: always
Cheers,
Stan H.
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Question 986174: How to find the perimeter of
Y=-5
X=-4
2y=x+8
X+y=4
Y=2x-5

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HOW? The five lines intersect to form a five sided figure. Find each adjascent intersection point, and use Distance Formula for each segment. Sum them. Much work but not complicated. Best is start by plotting the lines and maybe identifying the intersection points may be easier. Maybe fewer computations this way, too.

Question 986173: How do you find the perimeter of 2y=x+8
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Equation of a line, perimeter of this makes no sense.

Question 985884: What is true about any point that is equidistant from the endpoints of a segment
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It's on the perpendicular bisector of the segment.
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Also, that point and the 2 end points form an isosceles triangle (unless it's on the segment).

Question 985823: Angle A=3x-10 and Angle B=x+40. angle A and B are corresponding angles formed by two parallel lines intersected by transversal. find x,and the measures of angles A and B
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Hi dear,
Recall that corresponding angles are equal
Therefore,
A=B
i.e,3x-10=x+40
3x-x=40+10
2x=50
x=25
measure if A=3(25)-10
=75-10
=65
measure of B=25+40
=65

Question 985338: Three points have coordinates A(2,5),B(10,9) and C(6,2) ,line two passes through C and is perpendicular to line one.find coordinates of the point of intersection of line one and line two
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Hi there,
I take it that line 1 is AB.
= 9-5/10-2 = 4/8 = 1/2
Using the line equation for AB
Using m = 1/2 and point A (2,5)
y - 5 = 1/2(x - 2)
y = 1/2x - 1 + 5
y = 1/2x + 4
This is the equation for line AB
Line C has a gradient of -2
Lines that are perpendicular have
gradients that multiply together to give -1
m1 x m2 = -1
1/2 x m2 = -1
m2 = -2
...........
Using the line equation:
y - b = m(x - a)
Using m = -2 and pt C (6,2)
y - 2 = -2(x - 6)
y = -2x + 12 + 2
y = -2x + 14
This the equation of line C
Setting up simultaneous equations:
y - 1/2x = 4 ....(1)
y + 2x = 14 .....(2)
Multiply (1) by 4
4y - 2x = 16 .....(1)
y + 2x = 14 .....(2)
5y = 30
y = 6
Substitute y = 6 into:
y + 2x = 14
6 + 2x = 14
2x = 14 - 6
2x = 8
x = 4
{4,6} the point of intersection
of line AB and C
Hope this helps:-)

Which equation represents a line that is perpendicular to the line whose equation is 3x - 2y = 7?

a) y = (-3/2)x + 5
b) y = (3/2)x - 5
c) y = (-2/3)x + 4
d) y = (2/3)x - 4

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Calculate the slope of your given equation. Perpendicular lines have negative reciprocal slopes.

John

My calculator said it, I believe it, that settles it

Question 984977: What is straight and never-ending in two directions?

Question 984695: Find the value of the variable and YZ if Y is between X and Z.
XY=11, YZ=4C,XZ=83

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Assuming Y is between X and Y along a straight line,
XY+YZ=XZ
11+YZ=83
YZ =72
but YZ = 4C
4C=72
C=18

Question 984302: An equilateral triangle has its centroid at origin and one side is on the line x+y=1. Find the equations of other sides.
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An equilateral triangle has its centroid at origin and one side is on the line x+y=1. Find the equations of other sides.
--------------
The perpendicular bisector of the given side is y = x
----------------
Then intersection of the bisector and the line x+y = 1 is at (0.5,0.5)
The distance from the centroid to the vertex on y = x is 2x the distance from the origin to the line --> the vertex is at (-1,-1)
------
The slope of x+y=1 is -1 --> the tangent of the angle with the x-axis = 135 degs
--
The angles of the 2 other sides with the x-axis are 75 degs and 195 degs.
The slope of a line = the tangent of the angle with the x-axis.
----
Find the eqns of the lines thru (-1,-1) with slopes of the atan(75) and atan(195).
-------------------
= slope
--> y + 1 = (2 - sqrt(3))*(x + 1) ***** eqn of 1 line
---------------
= slope
--> y + 1 = (2 + sqrt(3))*(x + 1) ***** eqn of the other line

Question 984375: 2x+4x=12
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2x+4x=12
6x=12
divide both sides by 6
1x=2
x=2
;
check
4+8=12

Question 984186: Draw and label a figure for each relationship.
Point T lies on line WR.

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Draw a straight line. Mark two points on the line and label them W and R. Mark another point on the line. Label it T.

John

My calculator said it, I believe it, that settles it

Question 984187: Replace each _ with >,<, or = to make a true statement.
2.5 cm _ 28 mm.

Answer by Edwin McCravy(13211)   (Show Source):
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To change from centimeeters to millimeters move the decimal one place right:

2.5 cm = 25 mm < 28 mm

Edwin

Question 984163: Draw the graph of the line y = 10x + 10
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A point quickly read from the equation is (0,10). Slope also read from it is 10.

Plot the point (0,10), and find any other point according to vertical change of 10 for horizontal change of 1; plot this point;
Draw the line to connect the two (or more) points.

A closer look at the y-intercept

Question 984162: Find the equation of the straight line that goes through the following points
(1:20) (5:60)

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(1) Find value for the slope, and this may be called variable m.

(2) Choose either point, and fill values into point-slope form for a linear equation, y-v=m(x-u), for whichever point (u,v) you choose.

(3) Simplify, and put the equation into the form or format you want.