Question

is hijk a kite? justify your answer. yes, $overline{hi}$ is congruent to $overline{jk}$, and $overline{hk}$ is congruent to $overline{ij}$. yes, $overline{hi}$ is congruent to $overline{hk}$, and $overline{ij}$ is congruent to $overline{jk}$. no, $overline{hk}$ is not congruent to $overline{jk}$, and $overline{hi}$ is not congruent to $overline{ij}$. no, none of the sides are congruent.

Explanation:

Step1: Identify coordinates of vertices

Coordinates: $H(-1,1)$, $I(-10,-5)$, $J(2,-5)$, $K(10,3)$

Step2: Calculate side lengths (distance formula)

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

• $\overline{HI}$: $\sqrt{(-1 - (-10))^2+(1 - (-5))^2}=\sqrt{9^2+6^2}=\sqrt{81+36}=\sqrt{117}$
• $\overline{IJ}$: $\sqrt{(2 - (-10))^2+(-5 - (-5))^2}=\sqrt{12^2+0^2}=12$
• $\overline{JK}$: $\sqrt{(10-2)^2+(3 - (-5))^2}=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}$
• $\overline{HK}$: $\sqrt{(10 - (-1))^2+(3-1)^2}=\sqrt{11^2+2^2}=\sqrt{121+4}=\sqrt{125}$

Step3: Check kite definition

A kite has two distinct pairs of congruent adjacent sides. All calculated side lengths are unique, so no congruent pairs.

Answer:

No, none of the sides are congruent.