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:

$A(x_A;\ y_A),\ B(x_B,\ y_B)\\\\P_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)$

We have:

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

Answer: C. (4, -1)