Question

1. find the distance between the two points. write your answer as a decimal rounded to the hundredths place if needed.

(-7, 3) and (0, -6)

Explanation:

Step1: Recall distance formula

The distance $d$ 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: Assign point coordinates

Let $(x_1,y_1)=(-7,3)$ and $(x_2,y_2)=(0,-6)$.

Step3: Substitute into formula

$$d=\sqrt{(0-(-7))^2+(-6-3)^2}$$

Step4: Simplify inside the root

$$d=\sqrt{(7)^2+(-9)^2}=\sqrt{49+81}=\sqrt{130}$$

Step5: Calculate decimal value

$\sqrt{130}\approx11.40$

Answer:

11.40