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 parallelogram with nonperpendicular and noncongruent adjacent sides. if the vertex c(11, - 1) were shifted to the point c(11, 1), quadrilateral abcd would be a parallelogram with nonperpendicular adjacent sides

Explanation:

Step1: Calculate side - lengths

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For side $AB$ with $A(11,-7)$ and $B(9,-4)$:
$AB=\sqrt{(9 - 11)^2+(-4+7)^2}=\sqrt{(-2)^2 + 3^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $BC$ with $B(9,-4)$ and $C(11,-1)$:
$BC=\sqrt{(11 - 9)^2+(-1 + 4)^2}=\sqrt{2^2+3^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $CD$ with $C(11,-1)$ and $D(13,-4)$:
$CD=\sqrt{(13 - 11)^2+(-4 + 1)^2}=\sqrt{2^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}$.
For side $DA$ with $D(13,-4)$ and $A(11,-7)$:
$DA=\sqrt{(11 - 13)^2+(-7 + 4)^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}$.
All side - lengths are equal, so it could be a rhombus or a square.

Step2: Calculate slopes of adjacent sides

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Slope of $AB$, $m_{AB}=\frac{-4+7}{9 - 11}=\frac{3}{-2}=-\frac{3}{2}$.
Slope of $BC$, $m_{BC}=\frac{-1 + 4}{11 - 9}=\frac{3}{2}$.
Since $m_{AB}\times m_{BC}=-\frac{9}{4}
eq - 1$, adjacent sides are not perpendicular.
So the quadrilateral is a rhombus with non - perpendicular adjacent sides.

Answer:

rhombus with nonperpendicular adjacent sides