Answer:
(-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 = [tex]\frac{-4-4}{4+6} =-0.8[/tex]
Slope of perpendicular line would be = [tex]\frac{1}{-0.8} =-1.25[/tex]
Equation of the line through R with slope -1.25 is
[tex]y-2=1.25(x-4)\\y =1.25x-3[/tex]
Out of the four options,
only (-4,-8) satisfies
because [tex]-8 =-1.25(-4)-3[/tex]
so answer is (-4,-8)
