Question

find the coordinates of the other endpoint of a segment with an endpoint of (13, 5) and midpoint (8, 3).
a (18, 1)
b (-5, -2)
c (3, 1)
d (18, 7)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $(x_1,y_1)=(13,5)$ and the mid - point $(x_m,y_m)=(8,3)$.

Step2: Find the x - coordinate of the other endpoint

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we get $8=\frac{13 + x_2}{2}$. Cross - multiply: $16 = 13+x_2$. Then $x_2=16 - 13=3$.

Step3: Find the y - coordinate of the other endpoint

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we get $3=\frac{5 + y_2}{2}$. Cross - multiply: $6 = 5+y_2$. Then $y_2=6 - 5 = 1$.

Answer:

C. $(3,1)$