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?
+91 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).
