Question

find the distance between the points j(-8, 0) and k(1, 4). the exact distance between the two points is □.

Explanation:

Step1: Identify distance - formula

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

Step2: Assign values

Here, $x_1=-8,y_1 = 0,x_2 = 1,y_2=4$. Substitute into the formula: $d=\sqrt{(1-(-8))^2+(4 - 0)^2}$.

Step3: Simplify the expression inside the square - root

First, $1-(-8)=1 + 8=9$ and $4 - 0 = 4$. Then $(1-(-8))^2+(4 - 0)^2=9^2+4^2=81 + 16=97$.

Step4: Calculate the distance

So, $d=\sqrt{97}$.

Answer:

$\sqrt{97}$