Question

find the distance between the two points rounding to the nearest tenth (if necessary).\\((-2, -5)\\) and \\((1, -1)\\)

Explanation:

Step1: Recall 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, \( x_1=-2,y_1 = - 5,x_2=1,y_2=-1 \).

Step2: Substitute values into formula

First, calculate \( x_2 - x_1=1-(-2)=1 + 2 = 3 \) and \( y_2 - y_1=-1-(-5)=-1 + 5 = 4 \). Then, substitute into the formula: \( d=\sqrt{(3)^2+(4)^2} \).

Step3: Simplify the expression

Calculate \( 3^2 = 9 \) and \( 4^2 = 16 \), so \( d=\sqrt{9 + 16}=\sqrt{25} \).

Step4: Evaluate the square root

\( \sqrt{25}=5 \).

Answer:

5