Question

The midpoint of cd is -9,-10, endpoint c has coordinates of -1,9 what is the endpoint of d?

Answer 1

From c to the midpoint the coordinates have changed from (-1;9) to (-9;-10). So the difference is (-9-(-1); -10-(9)) that equals (-8;-19). And you should add (-8;-19) to the coordinates of the middle point (-9;-10). So we get (-9+(-8); -10+(-19)) that is (-17;-29). This is the endpoint of d. Answer: d (-17;-29).

Answer 2

`A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\The\ midpoint:M_(AB)\left((x_A+x_B)/(2);\ (y_A+y_B)/(2)\right)\\\\\\M_(CD)(-9;-10);\ C(-1;\ 9);\ D(x;\ y)\\\\(-1+x)/(2)=-9\ \ \ \ |multiply\ both\ sides\ by\ 2\\-1+x=-18\ \ \ \ |add\ 1\ to\ both\ sides\\x=-17\\\\(9+y)/(2)=-10\ \ \ \ \ |multiply\ both\ sides\ by\ 2\\9+y=-20\ \ \ \ |subtract\ 9\ from\ both\ sides\\y=-29\\\\Answer{\boxed{C(-17;-29)}`