Question

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

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

Step2: Calculate differences

$x_2 - x_1=4-(-5)=9$ and $y_2 - y_1=-5 - 4=-9$.

Step3: Square the differences

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

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 81=162$.

Step5: Calculate the square - root

$d=\sqrt{162}\approx 12.7$.

Answer:

$12.7$