Question

find the distance between the points (-4,5) and (-3,2). round to three decimal places. distance =

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, \( x_1=-4,y_1 = 5,x_2=-3,y_2 = 2 \).

Step2: Substitute values into formula

First, calculate \( x_2 - x_1=-3-(-4)=-3 + 4 = 1 \) and \( y_2 - y_1=2 - 5=-3 \). Then, substitute into the formula: \( d=\sqrt{(1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10} \).

Step3: Calculate and round

\( \sqrt{10}\approx3.16227766\). Rounding to three decimal places, we look at the fourth decimal place (2), which is less than 5, so we keep the first three decimals. So \( d\approx3.162 \).

Answer:

\( 3.162 \)