Question

shapes and distance examples

1. graph the right triangle with the point (3, -1) and (-5, 7) forming the hypotenuse. using the sides find the distance between the two points.

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, $(x_1,y_1)=(3,-1)$ and $(x_2,y_2)=(-5,7)$.

Step2: Calculate the differences

$x_2 - x_1=-5 - 3=-8$ and $y_2 - y_1=7-(-1)=8$.

Step3: Square the differences

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

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 64=128$.

Step5: Calculate the square - root

$d=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}$.

Answer:

$8\sqrt{2}$