Question

use the distance formula to find the distance between the two points. give an exact answer (not a decimal approximation). the distance between (1, 3) and (-3, -1) is

Explanation:

Step1: Identify the distance formula

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

Step2: Assign the values of the points

Let $(x_1,y_1)=(1,3)$ and $(x_2,y_2)=(-3,-1)$. Then $x_2 - x_1=-3 - 1=-4$ and $y_2 - y_1=-1 - 3=-4$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-4)^2 = 16$ and $(y_2 - y_1)^2=(-4)^2 = 16$. The sum is $16 + 16=32$.

Step4: Find the square - root

$d=\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$