Question

select the correct answers from each drop - down menu. complete the steps in the proof that show quadrilateral kite with vertices k(0, - 2), i(1,2), t(7,5), and e(4, - 1) is a kite. using the distance formula, ki = √((2 - (-2))²+(1 - 0)²)=√17, ke = √((4 - 0)²+((-1)-(-2))²)=√17, it = √((5 - 2)²+(7 - 1)²)=√45, and te = √((5 - (-1))²+(7 - 4)²)=√45. therefore, kite is a kite because

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 $KI$

For points $K(0,- 2)$ and $I(1,2)$, $x_1 = 0,y_1=-2,x_2 = 1,y_2 = 2$. Then $KI=\sqrt{(1 - 0)^2+(2-(-2))^2}=\sqrt{1 + 16}=\sqrt{17}$.

Step3: Calculate $KE$

For points $K(0,-2)$ and $E(4,-1)$, $x_1 = 0,y_1=-2,x_2 = 4,y_2=-1$. Then $KE=\sqrt{(4 - 0)^2+(-1-(-2))^2}=\sqrt{16 + 1}=\sqrt{17}$.

Step4: Calculate $IT$

For points $I(1,2)$ and $T(7,5)$, $x_1 = 1,y_1 = 2,x_2 = 7,y_2 = 5$. Then $IT=\sqrt{(7 - 1)^2+(5 - 2)^2}=\sqrt{36+9}=\sqrt{45}$.

Step5: Calculate $TE$

For points $T(7,5)$ and $E(4,-1)$, $x_1 = 7,y_1 = 5,x_2 = 4,y_2=-1$. Then $TE=\sqrt{(4 - 7)^2+(-1 - 5)^2}=\sqrt{9 + 36}=\sqrt{45}$.

Step6: Recall kite - property

A kite has two pairs of adjacent sides that are equal. Here $KI = KE=\sqrt{17}$ and $IT=TE=\sqrt{45}$.

Answer:

$KI=\sqrt{17}$, $KE=\sqrt{17}$, $IT=\sqrt{45}$, $TE=\sqrt{45}$