Question

A quadrilateral has vertices E(–4, 2), F(4, 7), G(8, 1), and H(0, –4). Which statements are true? Check all that apply.

The slope of EH is .
The slopes of EF and GH are both .
FG is perpendicular to GH.
Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
Quadrilateral EFGH is a rectangle because all angles are right angles.

Answer 1

Compute slopes:

- EH: (−4 − 2)/(0 − (−4)) = −6/4 = −3/2. — True (slope = −3/2).
- EF: (7 − 2)/(4 − (−4)) = 5/8.
- GH: (1 − (−4))/(8 − 0) = 5/8. — True (EF and GH both have slope 5/8).
- FG: (1 − 7)/(8 − 4) = −6/4 = −3/2.

Now evaluate the statements:

- The slope of EH is −3/2. — True.
- The slopes of EF and GH are both 5/8. — True.
- FG is perpendicular to GH. — False (slopes −3/2 and 5/8, product = −15/16 ≠ −1).
- Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel. — True (EF ∥ GH and FG ∥ EH).
- Quadrilateral EFGH is a rectangle because all angles are right angles. — False (adjacent slopes 5/8 and −3/2 are not negative reciprocals).