Question

example 3 find the distance between each pair of points. 21. v(5, 7) u(-1, -1) 22. m(4, 0) l(-2, -3) 23. j(-1, 4) k(2, -4)

Explanation:

Step1: Recall 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: Solve for problem 21

Let $(x_1,y_1)=(-1,-1)$ and $(x_2,y_2)=(5,7)$. Then $d=\sqrt{(5 - (-1))^2+(7 - (-1))^2}=\sqrt{(5 + 1)^2+(7 + 1)^2}=\sqrt{6^2+8^2}=\sqrt{36 + 64}=\sqrt{100}=10$.

Step3: Solve for problem 22

Let $(x_1,y_1)=(-2,-3)$ and $(x_2,y_2)=(4,0)$. Then $d=\sqrt{(4-(-2))^2+(0 - (-3))^2}=\sqrt{(4 + 2)^2+(0+3)^2}=\sqrt{6^2+3^2}=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}$.

Step4: Solve for problem 23

Let $(x_1,y_1)=(-1,4)$ and $(x_2,y_2)=(2,-4)$. Then $d=\sqrt{(2-(-1))^2+(-4 - 4)^2}=\sqrt{(2 + 1)^2+(-8)^2}=\sqrt{3^2+64}=\sqrt{9 + 64}=\sqrt{73}$.

Answer:

1. $10$
2. $3\sqrt{5}$
3. $\sqrt{73}$