Question

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

They are perpendicular because their slopes are equal.
They are perpendicular because their slopes are negative reciprocals.
They are not perpendicular because their slopes are equal.
They are not perpendicular because their slopes are negative reciprocals.

Answer 1

Answer:b

Step-by-step explanation:

they are not perpendicular

Answer 2

Answer:

The correct answer is they are perpendicular because their slopes are negative reciprocals .

Step-by-step explanation:

Explanation :

From the graph we have ,

F = (-4 , 0) , G = (4, 2 ) , C (-2 , 4) and D (0,-4 )

Slope  of line = $\frac{y_2-y_1}{x_2-x_1}$

Step 1:

FG is a line where  coordinate of F is (-4 , 0 )  and coordinate of G is (4,2).

Slope of line FG ($m_1$)  = $\frac{2 -0}{4 -(-4)}$ = $\frac{2}{8} = \frac{1}{4}$ .

Similarly , slope of line CD   ($m_2$) = $\frac{-4- 4}{0+2}$ = $\frac{-8}{2} = \frac{-4}{1}$

[Where coordinate of C is (-2,4) and D is (0,-4)]

Therefore , relation between slope of CD and FG  is ,

 ⇒$m_1 = \frac{-1}{m_2}$  

Final answer:

Hence , they are perpendicular because their slopes are equal .

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