Question

find the distance between the points (10, -10) and (-6, 4). round decimals to the nearest tenth. units

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 $(x_1,y_1)=(10,-10)$ and $(x_2,y_2)=(-6,4)$. Then $x_2 - x_1=-6 - 10=-16$ and $y_2 - y_1=4-(-10)=14$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-16)^2 = 256$ and $(y_2 - y_1)^2=14^2 = 196$.

Step4: Add the results

$(x_2 - x_1)^2+(y_2 - y_1)^2=256 + 196=452$.

Step5: Calculate the square - root

$d=\sqrt{452}\approx21.3$.

Answer:

$21.3$