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 = square root of 17. it = 45, and te = 45. therefore, kite is a kite because

Explanation:

Step1: Calculate distance formula for $KI$

$KI=\sqrt{(2 - (- 2))^{2}+(1 - 0)^{2}}=\sqrt{(4)^{2}+(1)^{2}}=\sqrt{16 + 1}=\sqrt{17}$

Step2: Calculate distance formula for $KE$

$KE=\sqrt{(4 - (-2))^{2}+(-1 - 0)^{2}}=\sqrt{(6)^{2}+(-1)^{2}}=\sqrt{36+1}=\sqrt{37}$

Step3: Calculate distance formula for $IT$

$IT=\sqrt{(7 - 2)^{2}+(5 - 1)^{2}}=\sqrt{(5)^{2}+(4)^{2}}=\sqrt{25 + 16}=\sqrt{41}$

Step4: Calculate distance formula for $TE$

$TE=\sqrt{(7 - 4)^{2}+(5-(-1))^{2}}=\sqrt{(3)^{2}+(6)^{2}}=\sqrt{9 + 36}=\sqrt{45}$
In a kite, two - pairs of adjacent sides are equal. Here, we assume the property of a kite is based on equal adjacent - side lengths. Since we have found the lengths, we match with the given blanks.

Answer:

$KI=\sqrt{17}$, $KE=\sqrt{37}$, $IT=\sqrt{41}$, $TE=\sqrt{45}$