Question

What is the most precise name for quadrilateral ABCD with vertices A(−1,0), B(4,0), C(5,4), and D(0,4)?A. rectangleB. parallelogramC. rhombusD. square

Answer 1

First thing to do is to plot the points into the rectangular coordinate system.

and join the points with a straight line.

The image will be :

It shows that the opposite sides are parallel to each other without a 90 degree angles.

So Option A and D will be eliminated.

A rhombus is a parallelogram that has 4 equal sides.

Let's check the side lengths using the distance formula

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}`

Distance between C(5, 4) and D(0, 4) :

`\begin{gathered} d=\sqrt[]{(4-4)^2+(0-5)^2}=\sqrt[]{25} \\ d=5 \end{gathered}`

Distance between B(4, 0) and C(5, 4) :

`\begin{gathered} d=\sqrt[]{(4-0)^2+(5-4)^2}=\sqrt[]{16+1} \\ d=\sqrt[]{17} \end{gathered}`

Since the sides are not equal. Option C is also eliminated.

Therefore, the answer is Choice B. Parallelogram