Question

find the length of the segment. round decimals to the nearest hundredth.

1. cd¯
2. ab¯

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: Calculate length of $\overline{AB}$

For points $A(-2,3)$ and $B(1,1)$, $x_1=-2,y_1 = 3,x_2=1,y_2 = 1$. Then $d_{AB}=\sqrt{(1-(-2))^2+(1 - 3)^2}=\sqrt{(3)^2+(-2)^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.61$.

Step3: Calculate length of $\overline{CD}$

For points $C(-4,-3)$ and $D(3,4)$, $x_1=-4,y_1=-3,x_2 = 3,y_2=4$. Then $d_{CD}=\sqrt{(3-(-4))^2+(4-(-3))^2}=\sqrt{(7)^2+(7)^2}=\sqrt{49+49}=\sqrt{98}\approx9.90$.

Answer:

Length of $\overline{AB}\approx3.61$, Length of $\overline{CD}\approx9.90$