Question

quadrilateral abcd is shown below. which value of v can be used to prove that abcd is a parallelogram? 3 of 10 questic v = -1, because the slope of \overline{dc}=3 and the slope of \overline{ab}=3 v = -3, because the slope of \overline{dc}=-3 and the slope of \overline{ab}=3 v = 1, because the slope of \overline{dc}=-3 and the slope of \overline{ab}=-3 v = 3, because the slope of \overline{dc}=3 and the slope of \overline{ab}=-3

Explanation:

Step1: Calculate the slope of \(\overline{AB}\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(2,5)\) and \(B(3,2)\), \(m_{AB}=\frac{2 - 5}{3 - 2}=\frac{-3}{1}=-3\)

Step2: Calculate the slope of \(\overline{DC}\)

For points \(D(-2,v)\) and \(C(-1,-2)\), \(m_{DC}=\frac{-2 - v}{-1-(-2)}=\frac{-2 - v}{1}=-2 - v\)

Step3: Set slopes equal for parallelogram

In a parallelogram, \(m_{AB}=m_{DC}\). So \(-3=-2 - v\). Solving for \(v\):
\(v=-2 + 3=1\)

Answer:

\(v = 1\), because the slope of \(\overline{DC}=-3\) and the slope of \(\overline{AB}=-3\) (the third option)