Question

1. find the distance between the points (-5,8) and (1,4). your answer must be in simplest radical form.

Explanation:

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: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=1-(-5)=6$ and $y_2 - y_1=4 - 8=-4$.

Step3: Square the differences

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 16=52$.

Step5: Take the square - root and simplify

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

Answer:

$2\sqrt{13}$