Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-5,2) and (1,-6)

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

Let $(x_1,y_1)=(-5,2)$ and $(x_2,y_2)=(1,-6)$. Then $x_2 - x_1=1-(-5)=6$ and $y_2 - y_1=-6 - 2=-8$.

Step3: Calculate the squares

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-8)^2=64$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Calculate the distance

$d=\sqrt{100}=10$.

Answer:

$10$