Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-5,4) and (4,-8)

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, $x_1=-5,y_1 = 4,x_2 = 4,y_2=-8$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4-(-5)=9$, $y_2 - y_1=-8 - 4=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 144=225$.

Step5: Calculate distance

$d=\sqrt{225}=15$.

Answer:

$15$