Question

find the distance between the two points in simplest radical form. (-2, 3) and (6, -4)

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Here, \( x_1=-2,y_1 = 3,x_2=6,y_2=-4 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=6-(-2)=6 + 2=8 \) and \( y_2 - y_1=-4 - 3=-7 \).
Then, substitute these into the distance formula: \( d=\sqrt{(8)^2+(-7)^2} \).

Step3: Simplify the expression inside the square root

Calculate \( 8^2 = 64 \) and \( (-7)^2=49 \). Then, \( 64 + 49=113 \). So, \( d=\sqrt{113} \).

Answer:

\(\sqrt{113}\)