B is the midpoint of line AC and E is the midpoint of line BD. If A(-9,-4), C(-1,6), and E(-4,-3), what are the coordinates of D?

Question

Linear geometry homework question

Answer 1

To find a midpoint, simply add the x-endpoints together and divide by 2. Then add the y-endpints together and divide by 2. In this case, the result is (-5,1).

If you are given a midpoint and one of the endpoints and are asked to find the other endpoint, you can use Algebra on the averaging formula (see above) for midpoint.

However, this process can be simplified to: double the given midpoint value and subtract the corresponding endpoint value. In this case, it would be

2*(-4) - (-5) = -8 + 5 = -3 for the x-value,

and

2*(-3) - 1 = -6 -1 = -7 for the y-value,

resulting in (-3,-7).

This saves about 2 steps in the process.

Answer 2

B((-9 - 1)/2, (-4 + 6)/2 = B (-5, 1); D(x,y). Then -4 = (-5 + x)/2; x = -3; -3 = (1 + y)/2; y = -7. D(-3, - 7)