Question

what is the most specific name for the figure?
p(0,0)
q(2a,2b)
r(2c,2b)
s(2d,0)
rectangle
square
parallelogram
trapezoid

Explanation:

Step1: Recall the definitions

• Rectangle: A parallelogram with four right - angles.
• Square: A rectangle with all sides equal.
• Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
• Trapezoid: A quadrilateral with at least one pair of parallel sides.

Step2: Analyze the given figure

The \(y\) - coordinates of points \(Q(2a,2b)\) and \(R(2c,2b)\) are the same. So, the slope of the line segment \(QR\) is \(m_{QR}=\frac{2b - 2b}{2c - 2a}=0\).
The \(y\) - coordinates of points \(P(0,0)\) and \(S(2d,0)\) are the same. So, the slope of the line segment \(PS\) is \(m_{PS}=\frac{0 - 0}{2d-0}=0\).
Since \(m_{QR}=m_{PS}\), \(QR\parallel PS\).
We cannot be sure if \(QP\parallel RS\) (because the slope of \(QP\) is \(m_{QP}=\frac{2b - 0}{2a-0}=\frac{b}{a}\) and the slope of \(RS\) is \(m_{RS}=\frac{0 - 2b}{2d - 2c}=\frac{-b}{d - c}\), and we have no information to suggest \(a=d - c\)).

Answer:

Trapezoid