Question

find the distance between the points (4, -2) and (-2, -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 $(x_1,y_1)=(4, - 2)$ and $(x_2,y_2)=(-2,-10)$. Then $x_1 = 4,y_1=-2,x_2=-2,y_2 = - 10$.

Step3: Calculate differences

$x_2 - x_1=-2 - 4=-6$ and $y_2 - y_1=-10-(-2)=-10 + 2=-8$.

Step4: Square the differences

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

Step5: Sum the squared differences

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

Step6: Take the square - root

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

Answer:

10