Question

what is the distance between (-3, 1) and (4, -5)? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-3,1)$ and $(x_2,y_2)=(4,- 5)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4-(-3)=7$, $y_2 - y_1=-5 - 1=-6$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$, $(y_2 - y_1)^2=(-6)^2=36$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 36=85$.

Step5: Calculate the square - root and round

$d=\sqrt{85}\approx9.2$.

Answer:

$9.2$