Question

find the coordinates of the missing endpoint.
#7 midpoint of uv is m(4,-6)
u(7,-9), v____
#8 midpoint of xy is m(-3,5)
x(-8,-3), y____

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for $x$ - coordinate of $V$ in problem #7

Let $U(7,-9)$ and $M(4,-6)$, and $V(x,y)$. For the $x$ - coordinate, $\frac{7 + x}{2}=4$. Cross - multiply: $7 + x=8$, then $x=8 - 7=1$.

Step3: Solve for $y$ - coordinate of $V$ in problem #7

For the $y$ - coordinate, $\frac{-9 + y}{2}=-6$. Cross - multiply: $-9 + y=-12$, then $y=-12 + 9=-3$. So $V(1,-3)$.

Step4: Solve for $x$ - coordinate of $Y$ in problem #8

Let $X(-8,-3)$ and $M(-3,5)$, and $Y(x,y)$. For the $x$ - coordinate, $\frac{-8 + x}{2}=-3$. Cross - multiply: $-8 + x=-6$, then $x=-6 + 8 = 2$.

Step5: Solve for $y$ - coordinate of $Y$ in problem #8

For the $y$ - coordinate, $\frac{-3 + y}{2}=5$. Cross - multiply: $-3 + y = 10$, then $y=10+3 = 13$. So $Y(2,13)$.

Answer:

#7: V(1,-3)
#8: Y(2,13)