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.

AThe slope of EH is -8/5
BThe slopes of EF and GH are both 5/8
CFG is perpendicular to GH.
DQuadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
EQuadrilateral EFGH is a rectangle because all angles are right angles.

I believe that the best answer among the choices provided by the question is D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
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aquialaska aquialaska · Answer 2 · 2019-07-04T02:36:29-04:00

Answer:

Option B and D are correct.

Step-by-step explanation:

Given: Vertices of the Quadrilateral

E( -4 , 2 ) , F( 4 , 7 ) , G( 8 , 1 ) and H( 0 , -4 )

To find: Correct Statements.

Slope of EH = \(\frac{-4-2}{0-(-4)}=\frac{-6}{4}=\frac{-3}{2}\)

Slope of EF = \(\frac{2-7}{-4-4}=\frac{-5}{-8}=\frac{5}{8}\)

Slope of GH = \(\frac{-4-1}{0-8}=\frac{-5}{-8}=\frac{5}{8}\)

Slope of FG = \(\frac{7-1}{4-8}=\frac{6}{-4}=\frac{-3}{2}\)

Consider,

Slope of FG × Slope of GH

\(=\frac{-3}{2}\times\frac{5}{8}\)

\(=\frac{-15}{16} eq-1\)

Since, Product of their slope not equal to -1.

⇒ FG is not perpendicular to GH.

Clearly from above slope of EH = Slope of FG and Slope of EF = Slope of GH

⇒ EH ║ FG and EF ║ GH

⇒ EFGH is a Parallelogram.

Therefore, Option B and D are correct.