Question

Use the image to answer the question.

Lines l and n intersect at point upper A. Line l is increasing from left to right and line n is decreasing from left to right. The bottom angle at the point upper A has a right angle symbol.

Given that lines l
and n
are perpendicular, which of the following is part of the proof that l
and n
have slopes that are opposite reciprocals?

(1 point)
Responses

△ABC
is similar to △EDA
.
triangle cap A cap b cap c is similar to triangle cap e cap d cap A .

The slope of line l
is BCCA
and the slope of line n
is DEAD
.
The slope of line l is cap b cap c over cap c cap A and the slope of line n is cap d cap e over cap A cap d .

∠ABC≅∠DAE
angle cap A cap b cap c is congruent to angle cap d cap A cap e

BCCA=−DEAD
cap b cap c over cap c cap A is equal to negative cap d cap e over cap A cap d
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Answer 1

To determine which statement is part of the proof that lines \( l \) and \( n \) are perpendicular and have slopes that are opposite reciprocals, we should focus on the relationship between the angles formed by the intersection of the two lines.

Since lines \( l \) and \( n \) are perpendicular at point \( A \), their slopes will have a specific relationship. The correct response should express that the slopes are negative reciprocals of each other as a result of the angle relationship.

Considering the options provided:

1. "△ABC is similar to △EDA." - This doesn't relate to slopes or right angles specifically.

2. "The slope of line \( l \) is \( BCCA \) and the slope of line \( n \) is \( DEAD \)." - This states the slopes but does not connect the slopes to their relationship.

3. "The slope of line \( l \) is \( \frac{bc}{cA} \) and the slope of line \( n \) is \( \frac{de}{dA} \)." - This provides slope values but does not mention reciprocal relationships.

4. "∠ABC≅∠DAE." - This states the congruence of angles but is not directly relating to slopes.

5. "BCCA=−DEAD." - This clearly states that the slopes of the two lines are negative reciprocals of one another, which is the definition of perpendicular lines.

Thus, the correct response that is part of the proof that lines \( l \) and \( n \) have slopes that are opposite reciprocals is:

**BCCA = -DEAD.**