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 <1), quadrilateral abcd rhombus with nonperpendicular adjacent sides rectangle with noncongruent adjacent sides trapezoid with exactly one pair of parallel sides parallelogram with nonperpendicular and noncongruent adjacent sides. if the vertex c(11, - 1) were shifted to the point c(11,

Explanation:

Step1: Calculate the slopes of the sides

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Slope of $AB$ with $A(11,-7)$ and $B(9,-4)$: $m_{AB}=\frac{-4+7}{9 - 11}=\frac{3}{-2}=-\frac{3}{2}$.
Slope of $BC$ with $B(9,-4)$ and $C(11,-1)$: $m_{BC}=\frac{-1 + 4}{11 - 9}=\frac{3}{2}$.
Slope of $CD$ with $C(11,-1)$ and $D(13,-4)$: $m_{CD}=\frac{-4 + 1}{13 - 11}=-\frac{3}{2}$.
Slope of $DA$ with $D(13,-4)$ and $A(11,-7)$: $m_{DA}=\frac{-7 + 4}{11 - 13}=\frac{-3}{-2}=\frac{3}{2}$.

Step2: Analyze parallel - perpendicular and congruence

Parallel lines have equal slopes. $AB\parallel CD$ ($m_{AB}=m_{CD}=-\frac{3}{2}$) and $BC\parallel DA$ ($m_{BC}=m_{DA}=\frac{3}{2}$), so it is a parallelogram.
The product of the slopes of adjacent sides $m_{AB}\times m_{BC}=-\frac{3}{2}\times\frac{3}{2}=-\frac{9}{4}
eq - 1$, so adjacent sides are not perpendicular.
Length of $AB=\sqrt{(9 - 11)^2+(-4 + 7)^2}=\sqrt{(-2)^2+3^2}=\sqrt{4 + 9}=\sqrt{13}$.
Length of $BC=\sqrt{(11 - 9)^2+(-1 + 4)^2}=\sqrt{2^2+3^2}=\sqrt{4 + 9}=\sqrt{13}$. But we are given non - congruent adjacent sides in the description of the parallelogram in the problem.

Answer:

parallelogram with nonperpendicular and noncongruent adjacent sides