Question

the distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. use the distance formula, to find the distance between $(2,3)$ and $(10,-3)$. use the keypad to enter your answer in the box. the distance between $(2,3)$ and $(10,-3)$ is units.

Explanation:

Step1: Identify the values of coordinates

Let $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(10, - 3)$.

Step2: Substitute into the distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(10 - 2)^2+(-3 - 3)^2}$.

Step3: Calculate the values inside the square - root

First, $(10 - 2)^2=8^2 = 64$ and $(-3 - 3)^2=(-6)^2 = 36$. Then $d=\sqrt{64 + 36}$.

Step4: Simplify the square - root

$64+36 = 100$, so $d=\sqrt{100}=10$.

Answer:

10