Mathematics: Which point is on a line that passes through point r and is perpendicular to line pq?

Which point is on a line that passes through point

PinkDivaGirl02

13.03.2022

(-4,-8)

Step-by-step explanation:

Given is a picture with a point R and a line PQ

We have to find the point out of the 4 options lying on the perpendicular line to PQ through R

R is the point (4,2)

P is (-6,4) and Q is (4,-4)

Slope of PQ = $\frac{-4-4}{4+6} =-0.8$

Slope of perpendicular line would be = $\frac{1}{-0.8} =-1.25$

Equation of the line through R with slope -1.25 is

$y-2=1.25(x-4)\\y =1.25x-3$

Out of the four options,

only (-4,-8) satisfies

because -8 =-1.25(-4)-3

so answer is (-4,-8)

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