Question

find the distance between the points (7, 0) and (1, -4). write your answer as a whole number or a fully simplified radical expression. do not round. 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 of the points

Let $(x_1,y_1)=(7,0)$ and $(x_2,y_2)=(1, - 4)$. Then $x_1 = 7$, $y_1=0$, $x_2 = 1$, $y_2=-4$.

Step3: Substitute values into the formula

$d=\sqrt{(1 - 7)^2+(-4 - 0)^2}=\sqrt{(-6)^2+(-4)^2}$.

Step4: Calculate the squares

$(-6)^2 = 36$ and $(-4)^2=16$, so $d=\sqrt{36 + 16}$.

Step5: Add the numbers inside the square - root

$36+16 = 52$, so $d=\sqrt{52}$.

Step6: Simplify the radical

$52=4\times13$, so $\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$