Question

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

Explanation:

Step1: Identify the distance - formula

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

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-5 - 3=-8$;
$y_2 - y_1=-5 - 5=-10$.

Step3: Square the differences

$(x_2 - x_1)^2=(-8)^2 = 64$;
$(y_2 - y_1)^2=(-10)^2 = 100$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 100=164$.

Step5: Calculate the distance

$d=\sqrt{164}\approx12.8$.

Answer:

$12.8$