Question

find the distance between the two points in simplest radical form. (5, -4) and (-1, 4)

Explanation:

Step1: Identify the 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 the values of the points

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

Step3: Substitute into the formula

$d=\sqrt{(-6)^2 + 8^2}=\sqrt{36 + 64}$.

Step4: Simplify the expression inside the square - root

$\sqrt{36 + 64}=\sqrt{100}=10$.

Answer:

$10$