Question

find the distance between each pair of points. round to the nearest hundredth.

1. (-5, -3) and (6, -1)
2. (-4, 5) and (4, 0)
3. given the graph below, find gh.

find the midpoint between each pair of points.

1. (-1, -5) and (-5, 9)
2. (7, -2) and (-4, 2)
3. if m is the midpoint of (overline{xy}), find the coordinates of x if m(-3, -1) and y(-8, 6).
4. if r is the midpoint of (overline{qs}), (qr = 8x - 51) and (rs = 3x - 6), find (qs).

Explanation:

13.

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-4,5)$ and $(x_2,y_2)=(4,0)$.

Step2: Substitute values

$d=\sqrt{(4 - (-4))^2+(0 - 5)^2}=\sqrt{(4 + 4)^2+(- 5)^2}=\sqrt{8^2+(-5)^2}=\sqrt{64 + 25}=\sqrt{89}\approx9.43$

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(-1,-5)$ and $(x_2,y_2)=(-5,9)$.

Step2: Substitute values

$x=\frac{-1+( - 5)}{2}=\frac{-1-5}{2}=\frac{-6}{2}=-3$, $y=\frac{-5 + 9}{2}=\frac{4}{2}=2$. The mid - point is $(-3,2)$.

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $(x_1,y_1)=(7,-2)$ and $(x_2,y_2)=(-4,2)$.

Step2: Substitute values

$x=\frac{7+( - 4)}{2}=\frac{7-4}{2}=\frac{3}{2}=1.5$, $y=\frac{-2 + 2}{2}=0$. The mid - point is $(1.5,0)$

Answer:

$9.43$

15.