Question

use the distance formula to answer the following questions: (d = sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}) find the distance between each pair of points. round your answer to the nearest tenth, if necessary. 7) ((7,6),(0,2)) 8) ((4,2),(-6,-6)) 9) ((-5,1),(-3,1)) 10) ((-3,6),(2,1))

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 7

For the points $(7,6)$ and $(0,2)$, let $(x_1,y_1)=(7,6)$ and $(x_2,y_2)=(0,2)$. Then $d=\sqrt{(0 - 7)^2+(2 - 6)^2}=\sqrt{(-7)^2+(-4)^2}=\sqrt{49 + 16}=\sqrt{65}\approx 8.1$.

Step3: Solve for problem 8

For the points $(4,2)$ and $(-6,-6)$, let $(x_1,y_1)=(4,2)$ and $(x_2,y_2)=(-6,-6)$. Then $d=\sqrt{(-6 - 4)^2+(-6 - 2)^2}=\sqrt{(-10)^2+(-8)^2}=\sqrt{100 + 64}=\sqrt{164}\approx 12.8$.

Step4: Solve for problem 9

For the points $(-5,1)$ and $(-3,1)$, let $(x_1,y_1)=(-5,1)$ and $(x_2,y_2)=(-3,1)$. Then $d=\sqrt{(-3+5)^2+(1 - 1)^2}=\sqrt{(2)^2+(0)^2}=\sqrt{4}=2$.

Step5: Solve for problem 10

For the points $(-3,6)$ and $(2,1)$, let $(x_1,y_1)=(-3,6)$ and $(x_2,y_2)=(2,1)$. Then $d=\sqrt{(2 + 3)^2+(1 - 6)^2}=\sqrt{(5)^2+(-5)^2}=\sqrt{25+25}=\sqrt{50}\approx 7.1$.

Answer:

1. $d\approx 8.1$
2. $d\approx 12.8$
3. $d = 2$
4. $d\approx 7.1$