Question

1. find the distance between the two points. write your answer as a decimal rounded to the hundredths place if needed. (4, -9) and (-3, -7)

Explanation:

Step1: Recall distance formula

The distance $d$ between 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 values to variables

Let $(x_1,y_1)=(4,-9)$ and $(x_2,y_2)=(-3,-7)$. Substitute:
$d=\sqrt{(-3-4)^2+(-7-(-9))^2}$

Step3: Simplify inside the root

Calculate differences first:
$d=\sqrt{(-7)^2+(2)^2}=\sqrt{49+4}$

Step4: Compute final root value

Simplify and evaluate:
$d=\sqrt{53}\approx7.28$

Answer:

7.28