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=), ( it=), and ( te=). therefore, kite is a kite because

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Accepted Answer

# Explanation:
## Step1: Calculate $KE$
The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $K(0,-2)$ and $E(4,-1)$, we have $x_1 = 0,y_1=-2,x_2 = 4,y_2=-1$.
$$
\begin{align*}
KE&=\sqrt{(4 - 0)^2+(-1-(-2))^2}\
&=\sqrt{4^2+(1)^2}\
&=\sqrt{16 + 1}\
&=\sqrt{17}
\end{align*}
$$
## Step2: Calculate $IT$
For points $I(1,2)$ and $T(7,5)$, $x_1 = 1,y_1 = 2,x_2=7,y_2 = 5$
$$
\begin{align*}
IT&=\sqrt{(7 - 1)^2+(5 - 2)^2}\
&=\sqrt{6^2+3^2}\
&=\sqrt{36+9}\
&=\sqrt{45}=3\sqrt{5}
\end{align*}
$$
## Step3: Calculate $TE$
For points $T(7,5)$ and $E(4,-1)$, $x_1 = 7,y_1 = 5,x_2 = 4,y_2=-1$
$$
\begin{align*}
TE&=\sqrt{(4 - 7)^2+(-1 - 5)^2}\
&=\sqrt{(-3)^2+(-6)^2}\
&=\sqrt{9 + 36}\
&=\sqrt{45}=3\sqrt{5}
\end{align*}
$$
## Step4: Determine the reason for $KITE$ being a kite
A kite is a quadrilateral with two pairs of adjacent sides equal. Here $KI = KE=\sqrt{17}$ and $IT=TE = 3\sqrt{5}$

# Answer:
$KE=\sqrt{17}$, $IT = 3\sqrt{5}$, $TE=3\sqrt{5}$. Therefore, $KITE$ is a kite because  $KI = KE$ and $IT=TE$ (two pairs of adjacent sides are equal).

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate \(KE\)

Step2: Calculate \(IT\)

Step3: Calculate \(TE\)

Step4: Determine the reason for \(KITE\) being a kite

Answer: