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.
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.

Answer 1

Answer:

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

B) The slopes of EF and GH are both 5/8

Step-by-step explanation:

The following inference can be made about each answer choices:

For option A

A) The slope of EH is 3/2 and not -8/5

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

For option B

B) The slopes of EF and GH are both 5/8

slope of a graph can be determined by change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For option C

C) FG is perpendicular to GH, its can't be determined since it is concluded that the quadrilateral is a parallelogram, therefore this option is wrong.

For option D

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

Slope of a graph can be determined by rise divided by run change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

for FG, slope =  (7-1)/(8-4) = 6/4 =3/2

EF and GH give the same slope, likewise EH and FG and they are opposite to each other, this make them parallel. Therefore, EFGH is a parallelogram.

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