Question

a rectangle has vertices $w(-1, -4)$, $x(-1, -1)$, $y(1, 1)$, and $z(1, -4)$.another rectangle has vertices $a(1, 1)$, $b(1, 3)$, $c(4, 3)$, and $d(4, 1)$.are the figures similar? remember the sides must be proportional.are the figures congruent?yesno

Explanation:

Step1: Calculate sides of first rectangle

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Length $WX$: $\sqrt{(-1-(-1))^2+(-1-(-4))^2}=\sqrt{0+9}=3$
Width $ZW$: $\sqrt{(-1-1)^2+(-4-(-4))^2}=\sqrt{4+0}=2$

Step2: Calculate sides of second rectangle

Length $AB$: $\sqrt{(1-1)^2+(3-1)^2}=\sqrt{0+4}=2$
Width $DA$: $\sqrt{(1-4)^2+(1-1)^2}=\sqrt{9+0}=3$

Step3: Check side proportionality

Ratio of lengths: $\frac{WX}{AB}=\frac{3}{2}$
Ratio of widths: $\frac{ZW}{DA}=\frac{2}{3}$
$\frac{3}{2}
eq \frac{2}{3}$, so sides not proportional. Congruent figures require equal sides, which these do not have.

Answer:

Are the figures similar? No
Are the figures congruent? No