Question

midpoint formula. used to find the midpoint between two points (x1, y1) and (x2, y2). formula: (\\(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\\)). 4. find the midpoint of \\(\overline{gh}\\) given g(7, -5) and h(9, -1). 5. find the midpoint of \\(\overline{ab}\\) given a(-7, 4) and b(3, -4).

Explanation:

Step1: Recall mid - point formula

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

Step2: Solve for mid - point of $\overline{GH}$

For points $G(7,-5)$ and $H(9,-1)$, $x_1 = 7$, $y_1=-5$, $x_2 = 9$, $y_2=-1$.
$x$ - coordinate of mid - point: $\frac{7 + 9}{2}=\frac{16}{2}=8$.
$y$ - coordinate of mid - point: $\frac{-5+( - 1)}{2}=\frac{-5 - 1}{2}=\frac{-6}{2}=-3$.
The mid - point of $\overline{GH}$ is $(8,-3)$.

Step3: Solve for mid - point of $\overline{AB}$

For points $A(-7,4)$ and $B(3,-4)$, $x_1=-7$, $y_1 = 4$, $x_2 = 3$, $y_2=-4$.
$x$ - coordinate of mid - point: $\frac{-7 + 3}{2}=\frac{-4}{2}=-2$.
$y$ - coordinate of mid - point: $\frac{4+( - 4)}{2}=\frac{4 - 4}{2}=0$.
The mid - point of $\overline{AB}$ is $(-2,0)$.

Answer:

1. $(8,-3)$
2. $(-2,0)$