Question

question find the distance between the two points in simplest radical form. (-1, -3) and (7, 5) answer attempt 1 out of 2 submit answer watch video show ex

Explanation:

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, $x_1=-1,y_1 = - 3,x_2=7,y_2 = 5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=7-(-1)=8$ and $y_2 - y_1=5 - (-3)=8$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{8^2 + 8^2}=\sqrt{64+64}=\sqrt{128}$.

Step4: Simplify the radical

$\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}$.

Answer:

$8\sqrt{2}$