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 =, it =, and te = 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 $TE$

For points $T(7,5)$ and $E(4, - 1)$, we have $x_1 = 7,y_1 = 5,x_2=4,y_2=-1$. Then $TE=\sqrt{(4 - 7)^2+(-1 - 5)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9 + 36}=\sqrt{45}$.

Step3: Calculate $KE$

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

Step4: Recall kite - property

A kite has two pairs of adjacent sides that are equal. We need to check other side - lengths too, but for the blanks given, we have filled them as above.

Answer:

The first blank: $\sqrt{45}$; the second blank: $\sqrt{17}$; the third blank: In a kite, two pairs of adjacent sides are equal.