Question

3a) point g is (502, 27); point h is (-457, 67). what are the coordinates of the mid - point of $overline{gh}$? 3b) $overline{er}$ has mid - point (5, 9) and an endpoint at (-1, -3). what are the coordinates of the other endpoint of $overline{er}$?

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 3a

Let $G(x_1,y_1)=(502,27)$ and $H(x_2,y_2)=(-457,67)$.
The $x$ - coordinate of the mid - point is $\frac{502+( - 457)}{2}=\frac{502 - 457}{2}=\frac{45}{2}=22.5$.
The $y$ - coordinate of the mid - point is $\frac{27 + 67}{2}=\frac{94}{2}=47$.
So the mid - point of $\overline{GH}$ is $(22.5,47)$.

Step3: Solve 3b

Let the mid - point $M(x_m,y_m)=(5,9)$ and one endpoint $E(x_1,y_1)=(-1,-3)$. Let the other endpoint be $R(x_2,y_2)$.
Using the mid - point formula for the $x$ - coordinate: $\frac{-1+x_2}{2}=5$. Cross - multiply: $-1+x_2 = 10$, then $x_2=11$.
Using the mid - point formula for the $y$ - coordinate: $\frac{-3+y_2}{2}=9$. Cross - multiply: $-3+y_2 = 18$, then $y_2=21$.
So the other endpoint of $\overline{ER}$ is $(11,21)$.

Answer:

3a. $(22.5,47)$
3b. $(11,21)$