Question

distance formula hw 2
find the distance between each pair of points.
1)
2)

1. (7, - 1), (2, 4)
2. (8, 8), (2, 4)

Explanation:

Step1: Recall 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: Solve for 3)

For points $(7,-1)$ and $(2,4)$, let $(x_1,y_1)=(7,-1)$ and $(x_2,y_2)=(2,4)$. Then $d=\sqrt{(2 - 7)^2+(4-( - 1))^2}=\sqrt{(-5)^2+(5)^2}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}$.

Step3: Solve for 4)

For points $(8,8)$ and $(2,4)$, let $(x_1,y_1)=(8,8)$ and $(x_2,y_2)=(2,4)$. Then $d=\sqrt{(2 - 8)^2+(4 - 8)^2}=\sqrt{(-6)^2+(-4)^2}=\sqrt{36+16}=\sqrt{52}=2\sqrt{13}$.

Answer:

1. $5\sqrt{2}$
2. $2\sqrt{13}$