Question

Quadrilateral EFGH is on a coordinate plane.Segment GH is on the line 2x+y=2, and segment FE is on the line 2x+y=4. Which statement proves how segments GH and FE are related?
A.They have slopes that are opposite reciprocals of 2 and -2 and are , therefore, perpendicular.

B. They have the same slope of 2 and are , therefore, parallel.

C. They have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular.

D. They have the same slope of -2 and are , therefore, parallel.

Answer 1

Answer: OPTION D.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

You know that the segment GH is on this line:

$2x+y=2$

Solving for "y", you get:

$y=-2x+2$

So you can identify that:

$m=-2\\b=2$

The segment FE is on this line:

$2x+y=4$

Solving for "y", you get:

$y=-2x+4$

Then you can identify that:

$m=-2\\b=4$

As you can notice, the lines have the same slope of $-2$. This means that they are parallel.

Answer 2

Answer: D

Option D

Step-by-step explanation: