Question

what is the distance between (-1,5) and (-3,-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, $(x_1,y_1)=(-1,5)$ and $(x_2,y_2)=(-3,-5)$.

Step2: Calculate differences

$x_2 - x_1=-3-(-1)=-3 + 1=-2$ and $y_2 - y_1=-5 - 5=-10$.

Step3: Square the differences

$(x_2 - x_1)^2=(-2)^2 = 4$ and $(y_2 - y_1)^2=(-10)^2 = 100$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 100=104$.

Step5: Calculate the square - root

$d=\sqrt{104}\approx10.2$.

Answer:

$10.2$