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.

A) The slope of EH is -8/5
B) The slopes of EF and GH are both 5/8
C) FG is perpendicular to GH.
D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.
E) Quadrilateral 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 · 2019-07-04T08:36:29+02:00

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 = [tex]\frac{-4-2}{0-(-4)}=\frac{-6}{4}=\frac{-3}{2}[/tex]

Slope of EF = [tex]\frac{2-7}{-4-4}=\frac{-5}{-8}=\frac{5}{8}[/tex]

Slope of GH = [tex]\frac{-4-1}{0-8}=\frac{-5}{-8}=\frac{5}{8}[/tex]

Slope of FG = [tex]\frac{7-1}{4-8}=\frac{6}{-4}=\frac{-3}{2}[/tex]

Consider,

Slope of FG × Slope of GH

[tex]=\frac{-3}{2}\times\frac{5}{8}[/tex]

[tex]=\frac{-15}{16}\neq-1[/tex]

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.