math qustion can u solve?

Question

if the line joining p1(2,3) andp2(7,9) is perpindicular to the line joining q1(8,k) and q2(2,4) find the value of k. how do u find the answer and what is the answer.....thank u very much

Answer 1

First find the slope of the first line using the slope formula:
m = (y2 - y1) / (x2 - x1)

Plug in your points (2,3) and (7,9):
m = (9-3) / (7-2)
m = 6/5

A *perpendicular* line has a slope that is the negative reciprocal.
m' = -5/6

Using the same slope formula with (2,4) and (8,k), your second line has the following slope:
m' = (k-4)/(8-2)
m' = (k-4)/6

But this needs to equal -5/6

-5/6 = (k-4)/6

Multiply both sides by 6:
k-4 = -5

Add 4 to both sides:
k = -5 + 4

Simplify:
k = -1

So k = -1 and the point q1 is therefore (8,-1)

Answer 2

The first two points p1 and p2 has a slope... let's say m1

m1=(9-3)/(7-2)
m1=6/5

You want perpendicular line so you want the slope of this line to be negative receprical of m1. Let's say m2

m2 = -1/(m1) = -1/(6/5) = -5/6

Back to the slope formula

-5/6=(4-k)/(2-8)
-5/6=(4-k)/-6
k=-1