Question

Geometry math question no Guessing and Please show work

Answer 1

If the point P(x, y) partitions the segment AB in the ratio 1 : 1, then the point P is midpoint of segment AB.

The formula of a midpoint of segment:

`A(x_A;\ y_A),\ B(x_B,\ y_B)\\\\P_(AB)\left((x_A+x_B)/(2);\ (y_A+y_B)/(2)\right)`

We have:

`A(13,\ 1)\to x_A=13,\ y_A=1\\B(-5,\ -3)\to x_B=-5,\ y_B-3\\\\P\left((13+(-5))/(2);\ (1+(-3))/(2)\right)\to P\left((8)/(2);\ (-2)/(2)\right)\to P(4,\ -1)`

Answer: C. (4, -1)