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Two lines m and n are parallel to each other and a line k intersects
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18 Feb 2025, 00:49
18 Feb 2025, 00:49
Expert Reply
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Question Stats:
62% (01:02) correct
37% (00:39) wrong based on 8 sessions
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Two lines m and n are parallel to each other and a line k intersects them. How many points are there in the same plane that have equal distances from all the three lines?
A. 1
B. 2
C. 3
D. 4
E. infinite
A. 1
B. 2
C. 3
D. 4
E. infinite
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Re: Two lines m and n are parallel to each other and a line k intersects
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11 Mar 2025, 11:28
11 Mar 2025, 11:28
Expert Reply
We have two lines $m$ and $n$ parallel to each other and a line $k$ intersects them, we get the figure as
As m and n are parallel lines, the distance between them is constant at all points, say 2 s units, so a point which is equidistance from line $m$ and line $n$ must be exactly in the middle of the line $m$ and line $n$ i.e. the point must be $s$ units away from line $m$ and $s$ units from line $n$.
Finally point which is $s$ units away from line $k$ as well as from line $m$ and line $n$ can be the required points, so there can be two such points, one on the left of line $k$ and the other one on the right of line k .
Hence the answer is (B).
As m and n are parallel lines, the distance between them is constant at all points, say 2 s units, so a point which is equidistance from line $m$ and line $n$ must be exactly in the middle of the line $m$ and line $n$ i.e. the point must be $s$ units away from line $m$ and $s$ units from line $n$.
Finally point which is $s$ units away from line $k$ as well as from line $m$ and line $n$ can be the required points, so there can be two such points, one on the left of line $k$ and the other one on the right of line k .
Hence the answer is (B).
gmatclubot
Re: Two lines m and n are parallel to each other and a line k intersects [#permalink]
11 Mar 2025, 11:28
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