Find the endpoint of segment GE if G is at (4,5) and the midpoint of the segment M is at (6,-2).

Question

Find the endpoint of segment GE if G is at (4,5) and the midpoint of the segment M is at (6,-2).

Answer 1

Hi Jessica, for each set of coordinates of a line segment, m = (a + b)/2, where m is the coordinate of the midpoint and a and b are the coordinates of the endpoints. Let's start with the x-coordinates. Then we have:

m = (a + b)/2

6 = (4 + b)/2

Now you can solve this equation for b, which is the x-coordinate of the other endpoint. Then use the same formula to do the same thing for the y-coordinates. Let me know if you have any trouble.

Answer 2

Plot the points on a coordinate plane. Draw a line connecting them, a vertical line down from (4,5), and a horizontal line left from (6,-2). The square of the vertical part of the resulting right triangle plus the square of the horizontal part will give you the square of the hypoteneus from (4,5) to (6,-2). Doubling that will give you the length of GE. So the length of GM is the square root of 7^2 + 2^2 or about 7.28, and the length of GE is about 14.56. Extending the vertical line downward until it is perpendicular to a horizontal line connecting with the extended hypoteneus will give you a right triangle with the point GE. Using a proportion will prove that the sides of the larger triangle are double those of the original. So the coordinates of GE are 4+4 and -2-7 or (8,-9).