Question

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

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 $(x_m,y_m)=(8,3)$. We need to find $(x_2,y_2)$.
For the x - coordinate:
$\frac{x_1 + x_2}{2}=x_m$, so $\frac{13 + x_2}{2}=8$.

Step2: Solve for x - coordinate of the other endpoint

Multiply both sides of the equation $\frac{13 + x_2}{2}=8$ by 2: $13 + x_2=16$.
Subtract 13 from both sides: $x_2=16 - 13=3$.

Step3: Solve for y - coordinate of the other endpoint

For the y - coordinate, $\frac{y_1 + y_2}{2}=y_m$, so $\frac{5 + y_2}{2}=3$.
Multiply both sides by 2: $5 + y_2=6$.
Subtract 5 from both sides: $y_2=6 - 5 = 1$.

Answer:

C. $(3,1)$