Question

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

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: Identify points for first - segment

For the segment with endpoints $(-2,-2)$ and $(1,3)$, let $(x_1,y_1)=(-2,-2)$ and $(x_2,y_2)=(1,3)$.

Step3: Substitute values into formula

$d=\sqrt{(1-(-2))^2+(3 - (-2))^2}=\sqrt{(1 + 2)^2+(3 + 2)^2}=\sqrt{3^2+5^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.8$.

Step4: Identify points for second - segment

For the second segment, assume endpoints are $(-4,3)$ and $(0,3)$ (from the graph). Let $(x_1,y_1)=(-4,3)$ and $(x_2,y_2)=(0,3)$.

Step5: Substitute values into formula

$d=\sqrt{(0-(-4))^2+(3 - 3)^2}=\sqrt{(0 + 4)^2+0^2}=\sqrt{4^2}=4$.

Answer:

For the first segment (with endpoints $(-2,-2)$ and $(1,3)$), the length is approximately $5.8$. For the second segment (assuming endpoints $(-4,3)$ and $(0,3)$), the length is $4$.