Question

If LaTeX: P\left(6,-2\right),\:Q\left(-2,\:8\right),\:R\left(-4,\:3\right),\:P ( 6 , − 2 ) , Q ( − 2 , 8 ) , R ( − 4 , 3 ) ,and LaTeX: S\left(-9,\:y\right)\:S ( − 9 , y )find the value of LaTeX: yy so that LaTeX: PQ\bot RS.

Answer 1

y = -1

Explanation:

First let us get the slope of the line PQ and RS

For PQ;

Given P(6, -2) and Q(-2,8)

slope m = 8-(-2)/-2-6

slope of pQ = 10/-8

slope of PQ = -5/4

For RS

R ( − 4 , 3 ) and S(-9, y)

slope of RS = y-3/-9+4

slope of RS = y-3/-5

For PQ to be perpendicular to RS, the product of their slope must be -1

Hence -5/4 (y-3/-5) = -1

y-3/4 = -1

cross multiply

y-3 = -4

y = -4+3

y = -1

Hence the value of y for PQ to be perpendicular to RS is -1