Question

find the endpoint of the segment with endpoint (4, 12) and midpoint (-1, 13)
(-4, -12)
(5, 13)
(13, -1)
(-6, 14)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $(x_1,y_1)=(4,12)$ be the given endpoint and $(x_m,y_m)=(-1,13)$ be the mid - point. We need to find $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $-1=\frac{4 + x_2}{2}$. Cross - multiply: $-1\times2=4 + x_2$. Then $x_2=-2 - 4=-6$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $13=\frac{12 + y_2}{2}$. Cross - multiply: $13\times2=12 + y_2$. Then $y_2 = 26-12 = 14$.

Answer:

$(-6,14)$