A line passes through the midpoint of $(1,2)$ and $(19,4)$. The line is perpendicular to a line through $(0,7)$ and $(4,-3)$. What is the $y$-coordinate of the line when $x=20$?

gueesstt
May 4, 2018

#1**+1 **

Midpoint of (1,2) , (19,4) = ( 10, 3)

The line containing points (0,7) and (4, - 3) has a slope of [ -3 - 7] / [4 - 0] = -10/4 = -5/2

So....a line perpendicular to this will have a slope of 2/5

So....the equation of this line is

y = (2/5)(x - 10) + 3

y = (2/5)x - 4 + 3

y = (2/5)x - 1

So....when x = 20

y = (2/5)(20) - 1

y = 8 - 1

y = 7

EDITED TO CORRECT A SIGN ERROR

CPhill
May 4, 2018