Question

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

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

Step2: Substitute the values into the formula

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

Step3: Simplify the expression inside the square root

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

Step4: Find the square root

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

Answer:

The distance between the two points is \( 5 \).