Question

A line segment has endpoints G(7, 1) and H(15, 3). The point M is the midpoint of GH. Which is the equation of the line perpendicular to GH and passing through M?

Answer 1

To determine the equation of the line perpendicular to line GH, we need to know the slope of line GH. We calculate it as follows:

mGH = 3 - 1 / 15 - 7 = 1/4

The slope of the line perpendicular is the negative reciprocal of the original slope. Therefore, the slope would be -4. 

The line passes through the midpoint of line GH. The points of the midpoint would be ( 7+15 /2 , 1+3 /2 ) = (11, 2).

y - 2 = -4(x - 11 )
y = -4x + 46