Question

find the distance between the points (4,-4) and (-3,1). round to three decimal places. distance =

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, \( x_1 = 4 \), \( y_1=-4 \), \( x_2=-3 \), \( y_2 = 1 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=-3 - 4=-7 \) and \( y_2 - y_1=1-(-4)=1 + 4 = 5 \).
Then, substitute these into the formula: \( d=\sqrt{(-7)^2+5^2} \).

Step3: Simplify the expression inside the square root

Calculate \( (-7)^2 = 49 \) and \( 5^2=25 \). Then, \( 49 + 25=74 \). So, \( d=\sqrt{74} \).

Step4: Calculate the decimal approximation

\( \sqrt{74}\approx8.602325 \). Rounding to three decimal places gives \( 8.602 \).

Answer:

\( 8.602 \)