Question

graph a right triangle with the two points forming the hypotenuse. using the sides, find the distance between the two points, to the nearest tenth (if necessary). (-1, -5) and (4, 7) 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(-1,-5)$ and $(x_2,y_2)=(4,7)$. Then $x_2 - x_1=4-(-1)=5$ and $y_2 - y_1=7 - (-5)=12$.

Step3: Calculate the squares

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=12^2=144$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 144=169$.

Step5: Calculate the square - root

$d=\sqrt{169}=13$.

Answer:

$13$