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 = $ 3 (square root of 5), and $te = $ 45, 117, 3 (square root of 5), square root of 117. therefore, kite is a kite because

Explanation:

Step1: Calculate $KE$ with distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. For $K(0,-2)$ and $E(4,-1)$:
$$KE=\sqrt{(-1-(-2))^2+(4-0)^2}=\sqrt{(1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}$$

Step2: Calculate $TE$ with distance formula

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

Step3: Define kite property

A kite has two distinct pairs of adjacent congruent sides.

Answer:

1. $KE =$ square root of 17
2. $TE =$ 3 (square root of 5)
3. KITE is a kite because it has two distinct pairs of adjacent sides that are equal in length ($KI=KE=\sqrt{17}$ and $IT=TE=3\sqrt{5}$)