Asked by oltr
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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.
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A horizontal line passes through point upper A. Point upper B is on the horizontal line and to the left of upper A. A vertical line segment extends from upper B down to point upper C on line l. Angle upper A upper B upper C has a right angle symbol. Point upper D is on the horizontal line and to the right of upper A. A vertical line segment extends from upper D down to point upper E on line n. Angle upper A upper D upper E has a right angle symbol.
Image Long DescriptionA horizontal line passes through point upper A. Point upper B is on the horizontal line and to the left of upper A. A vertical line segment extends from upper B down to point upper C on line l. Angle upper A upper B upper C has a right angle symbol. Point upper D is on the horizontal line and to the right of upper A. A vertical line segment extends from upper D down to point upper E on line n. Angle upper A upper D upper E 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
BCCA=−DEAD
start fraction cap b cap c over cap c cap A end fraction is equal to negative start fraction cap d cap e over cap A cap d end fraction
∠ABC≅∠DAE
angle cap A cap b cap c is congruent to angle cap d cap A cap e
The slope of line l
is BCCA
and the slope of line n
is DEAD
.
The slope of line l is start fraction cap b cap c over cap c cap A end fraction and the slope of line n is start fraction cap d cap e over cap A cap d end fraction .
△ABC
is similar to △EDA
.
triangle cap A cap b cap c is similar to triangle cap e cap d cap A .
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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.
▼Click for Long Desc
A horizontal line passes through point upper A. Point upper B is on the horizontal line and to the left of upper A. A vertical line segment extends from upper B down to point upper C on line l. Angle upper A upper B upper C has a right angle symbol. Point upper D is on the horizontal line and to the right of upper A. A vertical line segment extends from upper D down to point upper E on line n. Angle upper A upper D upper E has a right angle symbol.
Image Long DescriptionA horizontal line passes through point upper A. Point upper B is on the horizontal line and to the left of upper A. A vertical line segment extends from upper B down to point upper C on line l. Angle upper A upper B upper C has a right angle symbol. Point upper D is on the horizontal line and to the right of upper A. A vertical line segment extends from upper D down to point upper E on line n. Angle upper A upper D upper E 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
BCCA=−DEAD
start fraction cap b cap c over cap c cap A end fraction is equal to negative start fraction cap d cap e over cap A cap d end fraction
∠ABC≅∠DAE
angle cap A cap b cap c is congruent to angle cap d cap A cap e
The slope of line l
is BCCA
and the slope of line n
is DEAD
.
The slope of line l is start fraction cap b cap c over cap c cap A end fraction and the slope of line n is start fraction cap d cap e over cap A cap d end fraction .
△ABC
is similar to △EDA
.
triangle cap A cap b cap c is similar to triangle cap e cap d cap A .
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Answers
There are no human answers yet.
Answered by
GPT-5 mini
△ABC is similar to △EDA.
If the two right triangles are similar, then BC/BA = AD/DE. Since slope(l) = BC/BA and slope(n) = −DE/AD, it follows that slope(l) = −1/(slope(n)), i.e. the slopes are opposite reciprocals.
If the two right triangles are similar, then BC/BA = AD/DE. Since slope(l) = BC/BA and slope(n) = −DE/AD, it follows that slope(l) = −1/(slope(n)), i.e. the slopes are opposite reciprocals.
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