Question

find the length of the segments below. round to the nearest tenth (1 decimal place). 9. (1, 3) (-2, -2) 10.

Explanation:

Step1: Identify 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: Assign values

Let $(x_1,y_1)=(-2,-2)$ and $(x_2,y_2)=(1,3)$. Then $x_2 - x_1=1-(-2)=3$ and $y_2 - y_1=3 - (-2)=5$.

Step3: Calculate squares

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=5^2 = 25$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 25=34$.

Step5: Calculate distance

$d=\sqrt{34}\approx5.8$.

Answer:

$5.8$