Question

are ab and dc congruent? a (-4,1) b(-1,3) c (3,1) d(0,-1) a. yes b. no

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 AB

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

Step3: Calculate length of DC

For points $D(0,-1)$ and $C(3,1)$, $x_1=0,y_1=-1,x_2=3,y_2 = 1$. Then $DC=\sqrt{(3 - 0)^2+(1-(-1))^2}=\sqrt{(3)^2+(2)^2}=\sqrt{9+4}=\sqrt{13}$.

Step4: Compare lengths

Since $AB=\sqrt{13}$ and $DC=\sqrt{13}$, $AB$ and $DC$ are congruent.

Answer:

A. yes