Question

are $\triangle wxy$ and $\triangle qrs$ congruent?
yes
no

Explanation:

Step1: Identify coordinates of vertices

$\triangle WXY$: $W(9, -4)$, $X(2, 1)$, $Y(8, 8)$
$\triangle QRS$: $Q(-1, -4)$, $R(-9, 2)$, $S(-4, 8)$

Step2: Calculate side lengths (distance formula)

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

• For $\triangle WXY$:

$WX=\sqrt{(9-2)^2+(-4-1)^2}=\sqrt{49+25}=\sqrt{74}$
$XY=\sqrt{(8-2)^2+(8-1)^2}=\sqrt{36+49}=\sqrt{85}$
$YW=\sqrt{(9-8)^2+(-4-8)^2}=\sqrt{1+144}=\sqrt{145}$

• For $\triangle QRS$:

$QR=\sqrt{(-1+9)^2+(-4-2)^2}=\sqrt{64+36}=\sqrt{100}=10$
$RS=\sqrt{(-4+9)^2+(8-2)^2}=\sqrt{25+36}=\sqrt{61}$
$SQ=\sqrt{(-1+4)^2+(-4-8)^2}=\sqrt{9+144}=\sqrt{153}$

Step3: Compare corresponding side lengths

No set of sides from $\triangle WXY$ matches all sides of $\triangle QRS$.

Answer:

no