College Algebra Question

Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.

midpoint ​(10​,10), endpoint (12​,14​)

Answer 1

To answer this question, we must first know what the midpoint formula for 2 points in the coordinate plane. That formula is: (M_x,M_y) = ([x1+x2]/2, [y1+y2]/2). Essentially we take the average of the x coordinates and the average of the y coordinates to calculate the midpoint. In the problem description, we are given (M_x,M_y) = (10,10), and we are given one of the endpoints (x1,y1) = (12,14). If we construct 2 separate equations, one to find x2 and one to find y2, we can easily isolate and solve for these quantities.

[12+x2]/2=10, [12+x2]=20, x2=8

[14+y2]/2=10, [14+y2]=20, y2=6

Therefore, the other endpoint we are looking for is (x2,y2) = (8,6)