Question

find the distance between the two points. round to the nearest tenth. 8. a(13,2) and b(7,10) 9. g(-5,4) and h(2,6) 10. l(7,-1) and m(-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 problem 8

For points $A(13,2)$ and $B(7,10)$, let $(x_1,y_1)=(13,2)$ and $(x_2,y_2)=(7,10)$. Then $d=\sqrt{(7 - 13)^2+(10 - 2)^2}=\sqrt{(-6)^2+8^2}=\sqrt{36 + 64}=\sqrt{100}=10$.

Step3: Solve for problem 9

For points $G(-5,4)$ and $H(2,6)$, let $(x_1,y_1)=(-5,4)$ and $(x_2,y_2)=(2,6)$. Then $d=\sqrt{(2-(-5))^2+(6 - 4)^2}=\sqrt{(2 + 5)^2+2^2}=\sqrt{49+4}=\sqrt{53}\approx7.3$.

Step4: Solve for problem 10

For points $L(7,-1)$ and $M(-2,4)$, let $(x_1,y_1)=(7,-1)$ and $(x_2,y_2)=(-2,4)$. Then $d=\sqrt{(-2 - 7)^2+(4-(-1))^2}=\sqrt{(-9)^2+5^2}=\sqrt{81 + 25}=\sqrt{106}\approx10.3$.

Answer:

1. 10
2. 7.3
3. 10.3