Question

find the endpoint of the segment with the endpoint of (-4,5) and midpoint of (7, -9)
(1.5, -2)
(11,4)
(13, 18)
(18, -23)

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 $(x_1,y_1)=(-4,5)$ and $M=(7,-9)$, and we want to find $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=7$. Substitute $x_1=-4$ into the equation: $\frac{-4 + x_2}{2}=7$. Multiply both sides by 2: $-4 + x_2=14$. Then add 4 to both sides: $x_2=14 + 4=18$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-9$. Substitute $y_1 = 5$ into the equation: $\frac{5 + y_2}{2}=-9$. Multiply both sides by 2: $5 + y_2=-18$. Then subtract 5 from both sides: $y_2=-18 - 5=-23$.

Answer:

D. $(18,-23)$