Question

Choose the best selection for the

quadrilateral with vertices at the
following points:
(0,0), (-2,3), (7,0), (5,3)
Hint: Start by graphing the points.
Distance Formula: d= V(x² – x¹)² + (y² - y¹)²
A. Rectangle
B. Parallelogram
C. Rhombus
D. Trapezoid

Answer 1

By calculating the lengths of the sides of the quadrilateral using the distance formula, it is determined that the quadrilateral with vertices (0,0), (-2,3), (7,0), and (5,3) is a parallelogram, as opposite sides are equal in length.

Step-by-step explanation:

To determine the type of quadrilateral formed by the points (0,0), (-2,3), (7,0), and (5,3), we need to calculate the lengths of the sides and diagonals. Using the distance formula d= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, we find:

• The length of side AB between (0,0) and (-2,3) is \sqrt{(-2 - 0)^2 + (3 - 0)^2} = \sqrt{13}.

• The length of side BC between (-2,3) and (5,3) is \sqrt{(5 - (-2))^2 + (3 - 3)^2} = 7.

• The length of side CD between (5,3) and (7,0) is \sqrt{(7 - 5)^2 + (0 - 3)^2} = \sqrt{13}.

• The length of side DA between (7,0) and (0,0) is \sqrt{(0 - 7)^2 + (0 - 0)^2} = 7.

Since opposite sides are equal in length (AB = CD and BC = DA), we can conclude that the quadrilateral is a parallelogram. The absence of right angles excludes the possibility of it being a rectangle, and unequal diagonals exclude it from being a rhombus. It cannot be a trapezoid as both pairs of opposite sides are parallel and equal. Therefore, the best selection for the quadrilateral described is a B. Parallelogram.