Which statement best explains the relationship between lines FG and HJ?

D.

Step-by-step explanation:

From the figure, we have

The coordinates of the point F are: (-4,1).

The coordinates of the point G are: (0,-2)

The coordinates of the point J are: (0,4) and

The coordinates of the point H are: (-4,-2).

Now, the slope of the line FG is :

S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}S=

x

2

−x

1

y

2

−y

1

S=\frac{-2-1}{0+4}S=

0+4

−2−1

S=\frac{-3}{4}S=

4

−3

And, the slope of the line HJ is:

S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}S=

x

2

−x

1

y

2

−y

1

S=\frac{-2-4}{-4-0}S=

−4−0

−2−4

S=\frac{3}{2}S=

2

3

Now, the slope of FG=\frac{1}{slope of HJ}theslopeofFG=

slopeofHJ

1

\frac{-3}{4}=\frac{2}{3}

4

−3

=

3

2

which is not possible, thus They are not perpendicular because their slopes are not negative reciprocals.