Question

1. find the distance between the points (-5,8) and (1,4). your answer must be in simplest radical form.
2. find the slope of the line segment with endpoints at (-5,-1) and (-1,-3).
3. find the length and slope of $overline{gh}$.

$m = \frac{y^{2}-y^{1}}{x^{2}-x^{1}}$

Explanation:

36.

Step1: Identify 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, $x_1=-5,y_1 = 8,x_2=1,y_2 = 4$.

Step2: Substitute values

$d=\sqrt{(1-(-5))^2+(4 - 8)^2}=\sqrt{(1 + 5)^2+(-4)^2}=\sqrt{6^2+(-4)^2}$.

Step3: Calculate

$d=\sqrt{36 + 16}=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Step1: Identify slope - formula

The slope formula for a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-5,y_1=-1,x_2=-1,y_2=-3$.

Step2: Substitute values

$m=\frac{-3-(-1)}{-1-(-5)}=\frac{-3 + 1}{-1 + 5}$.

Step3: Calculate

$m=\frac{-2}{4}=-\frac{1}{2}$.

Step1: Identify distance - formula

Use $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, where $x_1=-4,y_1=-3,x_2=0,y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(0-(-4))^2+(1-(-3))^2}=\sqrt{4^2+4^2}$.

Step3: Calculate

$d=\sqrt{16 + 16}=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Slope:

Answer:

$2\sqrt{13}$

37.