SOLUTION: plz help me to solve this question..... Q. Three points have coordintes A(4,13), B(9,3) and C(10,8).Find the equation of (a) the line AB (b) the line through C perpendicular

Question 230539: plz help me to solve this question.....
Q. Three points have coordintes A(4,13), B(9,3) and C(10,8).Find the equation of
(a) the line AB
(b) the line through C perpendicular to the line y-4x=5.
the line through C meets the line AB at point P.Calculate the coordinates of P
and the ratio AP:PB

Found 2 solutions by algebrapro18, Alan3354:
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
In order to do this we will need to remember a few key facts:

1) the equation to find the slope is
2) the point slope formula for a line is y-y1=m(x-x1)
3) Perpendicular lines have opposite reciprical slopes
4) the slope intercept form of a line is y=mx+b

Now on to solving your problem.

Part A: Find the equation of the line AB.
Well we know point A and point B so we can find the slope by using equation 1.

m = (3-13)/(9-4) = -2

Now that we have the slope of the line and a point on the line we can use equation 2 to find the equation of the line.

y-y1=m(x-x1)
y-3=-2(x-9)

I will leave the simplification to you but you should end up with the equation being y=-2x+21.

Part B Subpart 1: Find the equation of the line through C perpendicular to line y-4x=5.

To do this we need to get the equation of the given line into slope-intercept form and then we can use fact 3 to find the slope of the line we are finding. To get the line into slope intercept form all we have to do is add 4x to both sides.

y = 4x+5

So we know this line has a slope of 4 so the line we are finding the equation of will have a slope of -1/4 by fact 3. Now that we have a point on the line and its slope we can use equation 2 again and find the equation of the line we are looking for. I will leave the algebra to you but you should get y=-1/4x+21/2 for your equation.

Part B Subpart 2: Find the point where the two lines we found intersect.

To do this we solve the system of equations.

y = -2x + 21
y = -1/4x + 21/2

Since both are equal to y we can set both equations equal and solve for x. I will leave the algebra for you to do but you should get that x = 6. NOw that we know x = 6 we can substitute that back into either equation. Again I will leave this for you to do but you should get y = 9. So point P is (6,9).

Now I'm not sure how to do the rest of this problem so I'm sorry. Let me know if you need more assistance.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Three points have coordintes A(4,13), B(9,3) and C(10,8).
Find the equation of
(a) the line AB
Find the slope, m
m = diffy/diffx = 10/-5
m = -2
------
Use either point to find b, then the eqn
y = mx+b to find b
13 = -2*4 + b
b = 21
y = -2x + 21 (Eqn of AB)
-------------
-------------
(b) the line through C perpendicular to the line y-4x=5.
y = 4x+5
m = -1/4 (slope perpendicular to m=4)
8 = -1/4*10 + b
b = 10.5
y = -(1/4)x + 10.5
------------
the line through C meets the line AB at point P.
Calculate the coordinates of P
y = -2x+21 = -x/4 + 10.5
1.75x = 10.5
x = 6
y = -12 + 21 = 9
P(6,9)
----------
and the ratio AP:PB
Since it's a straight, use the x values to get the ratio
A - 4
P - 6
B - 9
AP = 2
PB = 3
AP:PB = 2:3

RELATED QUESTIONS
Please help me solve this equation Find the distance between the given points. (- 3, 1)... (answered by Cromlix,Alan3354)
Determine whether the three points P(-6, -9, 4), Q(-8, -13, -2) and R(-10, -17, -10) are... (answered by KMST)
the midpoint of AB is M (3, 2). if the coordintes of A are (8, 7). what are the... (answered by greenestamps)
Find the slope of the line passing through the points (0, -4) and (-10, 9). a) 10/13 b) (answered by rfadrogane)
A circle through P(5,9), Q(11,-3), and R(13,3). Find its equation in standard form. To... (answered by josgarithmetic)
plz help me with this maths equation i will be really thankful Q) which of the following (answered by Theo)
Lessons Course Information Assessments Gradebook Email Discussion Groups ChatRoom... (answered by richard1234)
The problem consist of a diagram: A is parallel to B and C is parallel to D (A and B are... (answered by venugopalramana)
In advance I apologize for this long question and also thank you for helping me. Use... (answered by josgarithmetic)