Question

to the nearest hundredth, what is the distance between (-4, -7) and (3, 5)? enter the answer in the box.

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

Step2: Calculate differences

$x_2 - x_1=3-(-4)=7$ and $y_2 - y_1 = 5-(-7)=12$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=12^2 = 144$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 144=193$.

Step5: Calculate the square - root

$d=\sqrt{193}\approx13.89$.

Answer:

$13.89$