Find the point (x,y) on the line y=−2x+4 that is equidistant from the points (−6,−10) and (−3,−9).

Question

PLease help me with this!

Answer 1

(-27, 58) is on the given line and equidistant to the two given points

find the midpoint of (-6,10) and (-3,-9) = (-9/2,-19/2)

then find the line perpendicular to the line through (-6,-10) and (-3,-9) that goes through that midpoint

It's- y = -3x-23

set it equal to y=-2x+4 to find where they intersect

-3x-23 = -2x+4

x =-27

y = -2(-27)+4 = 58

the point is (-27, 58)