Question

find the distance between the points (10, 2) and (5, -10). round decimals to the nearest tenth. units

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: Assign values

Let $(x_1,y_1)=(10,2)$ and $(x_2,y_2)=(5, - 10)$. Then $x_2 - x_1=5 - 10=-5$ and $y_2 - y_1=-10 - 2=-12$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-5)^2 = 25$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 144=169$.

Step5: Find square - root

$d=\sqrt{169}=13$.

Answer:

13