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 = \\(\sqrt{(2-(-2))^{2}+(1 - 0)^{2}}=\sqrt{17}\\). ke = square root of 17. it = square root of 113. te = 45. therefore, kite is a kite because square root of 113 > square root of 17 and square root of 45 > square root of 17.

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 $IT$

For points $I(1,2)$ and $T(7,5)$, $IT=\sqrt{(7 - 1)^2+(5 - 2)^2}=\sqrt{6^2+3^2}=\sqrt{36 + 9}=\sqrt{45}$.

Step3: Calculate $TE$

For points $T(7,5)$ and $E(4,-1)$, $TE=\sqrt{(4 - 7)^2+(-1 - 5)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}$.

Step4: Analyze kite - property

In a kite, two pairs of adjacent sides are equal. Here $KI=\sqrt{17}$, $KE=\sqrt{17}$, $IT = \sqrt{45}$, $TE=\sqrt{45}$.

Answer:

The first blank is $\sqrt{45}$, the second blank is $\sqrt{45}$ (assuming we are filling in the lengths of $IT$ and $TE$ as per the kite - proof requirements).