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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?

 Apr 15, 2021
 #1
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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).

 Apr 15, 2021

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