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?

Question

help, i need help. I don't know how to solve this.

Answer 1

The midpoint of a line joining two points is the average of their coordinates: ((1+19)/2, (2+4)/2)=(10,3).

Gradient of the line: (7-(-3))/(0-4))=10/(-4)=-5/2. The slope of the perpendicular is the negative reciprocal of this=2/5.

Standard form of the required line is y=mx+b. Plug in (10,3) and m=2/5:

y-3=⅖(x-10)=2x/5-4, so y=2x/5-4+3=2x/5-1 is the equation of the perpendicular.

When x=20, y=7.