Question

select the correct answer from each drop - down menu. a quadrilateral has vertices a(11, - 7), b(9, - 4), c(11, - 1), and d(13, - 4). quadrilateral abcd is a quadrilateral abcd would be a kite. if the vertex c(11, - 1) were shifted to the point c(11, 1).

Explanation:

Step1: Calculate the lengths of the sides

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For side $AB$: $x_1 = 11,y_1=-7,x_2 = 9,y_2=-4$, $AB=\sqrt{(9 - 11)^2+(-4+7)^2}=\sqrt{(-2)^2 + 3^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $BC$: $x_1 = 9,y_1=-4,x_2 = 11,y_2=-1$, $BC=\sqrt{(11 - 9)^2+(-1 + 4)^2}=\sqrt{2^2+3^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $CD$: $x_1 = 11,y_1=-1,x_2 = 13,y_2=-4$, $CD=\sqrt{(13 - 11)^2+(-4 + 1)^2}=\sqrt{2^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $DA$: $x_1 = 13,y_1=-4,x_2 = 11,y_2=-7$, $DA=\sqrt{(11 - 13)^2+(-7 + 4)^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}$.

Step2: Determine the type of quadrilateral

Since $AB = BC=CD = DA=\sqrt{13}$, quadrilateral $ABCD$ is a rhombus.

Answer:

rhombus