Question

are bc and ad 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 BC

For points $B(-1,3)$ and $C(3,1)$, $x_1=-1,y_1 = 3,x_2=3,y_2 = 1$.
$d_{BC}=\sqrt{(3+ 1)^2+(1 - 3)^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}$.

Step3: Calculate length of AD

For points $A(-4,1)$ and $D(0,-1)$, $x_1=-4,y_1 = 1,x_2=0,y_2=-1$.
$d_{AD}=\sqrt{(0 + 4)^2+(-1 - 1)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5}$.

Step4: Compare lengths

Since $d_{BC}=d_{AD}=2\sqrt{5}$, segments BC and AD are congruent.

Answer:

A. yes