Question

find the distance between the two points rounding to the nearest tenth (if necessary). (3, -3) and (1, 5)

Explanation:

Step1: Identify 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: Substitute the values

Let $(x_1,y_1)=(3,-3)$ and $(x_2,y_2)=(1,5)$. Then $x_2 - x_1=1 - 3=-2$ and $y_2 - y_1=5-( - 3)=8$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-2)^2 = 4$ and $(y_2 - y_1)^2=8^2 = 64$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 64=68$.

Step5: Calculate the distance

$d=\sqrt{68}\approx 8.2$.

Answer:

$8.2$