Let F, G, and H, be collinear points on the Cartesian plane such that FG/GH=1 If F=(a, b) and H=(7a, c), then what is the x-coordinate of G?

Guest Apr 15, 2021

#1**0 **

I assume you would want me to answer in terms of a, b, and c.

The key realization is FG/GH=1 - this means FG = GH.

This also implies that if a line were to be drawn between the two points, point G would be the midpoint - meaning that the coordinates of point G are the averages of the endpoints of the line(point F and H).

The average of a and 7a is 4a.

The average of b and c is (b+c)/2

Therefore the coordinates of point G are **(4a,(b+c)/2)**.

ArithmeticBrains1234 Apr 15, 2021