Question

use the distance formula to find the distance between x(-3,1) and y(4,-4)? round your answer to the nearest tenth if necessary. distance =

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign the coordinates

Here, $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(4,-4)$.

Step3: Calculate the differences

$x_2 - x_1=4-(-3)=4 + 3=7$ and $y_2 - y_1=-4 - 1=-5$.

Step4: Square the differences

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=(-5)^2 = 25$.

Step5: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 25=74$.

Step6: Take the square - root

$d=\sqrt{74}\approx8.6$.

Answer:

$8.6$