Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points in simplest radical form. (7, 7) and (5, 2) click twice to draw a line. click a segment to erase it.

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(5,2)$ and $(x_2,y_2)=(7,7)$.

Step2: Calculate the differences

$x_2 - x_1=7 - 5 = 2$ and $y_2 - y_1=7 - 2 = 5$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=2^2 = 4$ and $(y_2 - y_1)^2=5^2 = 25$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 25=29$.

Step4: Take the square - root

$d=\sqrt{29}$.

Answer:

$\sqrt{29}$