Question

The coordinates of the vertices of quadrilateral ABCD are A(0, −4), B(−4, 3), C(3, 4), and D(6, −1).



Drag and drop the choices into each box to correctly complete the sentences.

The slope of AB¯¯¯¯¯ is ______ , the slope of BC¯¯¯¯¯ is ______, the slope of CD¯¯¯¯¯ is ______, and the slope of AD¯¯¯¯¯ is ______. Quadrilateral ABCD is _________________ because ______________.


A. - 7/4
B. - 5/3
C. 1/7
D. 1/2
E. a parallelogram
F. a trapezoid
G. neither a parallelogram nor a trapezoid
H. both pairs of opposite sides are parallel
I. only one pair of opposite sides is parallel
J. neither pair of opposite sides is parallel

Answer 1

To calculate the slopes of the sides of quadrilateral ABCD, we use the slope formula, which is:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

1. **Calculating the slope of AB:**
- Points A(0, -4) and B(-4, 3)
\[
\text{slope of } AB = \frac{3 - (-4)}{-4 - 0} = \frac{3 + 4}{-4} = \frac{7}{-4} = -\frac{7}{4}
\]
So the slope of AB is **-7/4**.

2. **Calculating the slope of BC:**
- Points B(-4, 3) and C(3, 4)
\[
\text{slope of } BC = \frac{4 - 3}{3 - (-4)} = \frac{1}{3 + 4} = \frac{1}{7}
\]
So the slope of BC is **1/7**.

3. **Calculating the slope of CD:**
- Points C(3, 4) and D(6, -1)
\[
\text{slope of } CD = \frac{-1 - 4}{6 - 3} = \frac{-5}{3}
\]
So the slope of CD is **-5/3**.

4. **Calculating the slope of AD:**
- Points A(0, -4) and D(6, -1)
\[
\text{slope of } AD = \frac{-1 - (-4)}{6 - 0} = \frac{-1 + 4}{6} = \frac{3}{6} = \frac{1}{2}
\]
So the slope of AD is **1/2**.

Now, we have:

- The slope of AB is **-7/4**.
- The slope of BC is **1/7**.
- The slope of CD is **-5/3**.
- The slope of AD is **1/2**.

Next, to determine the type of quadrilateral, we observe the slopes:

- The slopes of AB and CD do not match.
- The slopes of BC and AD also do not match.
- Therefore, there are no pairs of opposite sides that are parallel.

Thus, Quadrilateral ABCD is **neither a parallelogram nor a trapezoid** because **neither pair of opposite sides is parallel**.

Final Responses:

The slope of AB is **-7/4**, the slope of BC is **1/7**, the slope of CD is **-5/3**, and the slope of AD is **1/2**. Quadrilateral ABCD is **neither a parallelogram nor a trapezoid** because **neither pair of opposite sides is parallel**.