Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-6, -6) and (-8, 2)

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 $(x_1,y_1)=(-6,-6)$ and $(x_2,y_2)=(-8,2)$. Then $x_2 - x_1=-8-(-6)=-8 + 6=-2$ and $y_2 - y_1=2-(-6)=2 + 6 = 8$.

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

$d=\sqrt{68}\approx 8.246$.

Step6: Round to the nearest tenth

Rounding $8.246$ to the nearest tenth gives $8.2$.

Answer:

$8.2$