GATE CE 2022 Set 2 — Question 8
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Consider the following equations of straight lines: Line L1:
Line L2:
Line L3:
Line L4: Which one among the following is the correct statement?
Line L2:
Line L3:
Line L4: Which one among the following is the correct statement?
Correct answer
(D) L4 is perpendicular to L2 and L4 is parallel to L3
Solution
The slope of a line given by is .Slopes of the given lines:
Line L1:
Line L2:
Line L3:
Line L4: Parallelism: Lines are parallel if they have the same slope.
Here, . Thus, L1, L3, and L4 are parallel to each other.Perpendicularity: Lines are perpendicular if the product of their slopes is .
. Thus, L2 is perpendicular to L1.
Since L1, L3, and L4 are parallel, L2 is also perpendicular to L3 and L4.Evaluating the options:
(A) L1 is parallel to L2 (False, ).
(B) L2 is parallel to L4 (False, ).
(C) L3 is perpendicular to L4 (False, ).
(D) L4 is perpendicular to L2 (True, ) and L4 is parallel to L3 (True, ).Therefore, the correct option is (D).
Line L1:
Line L2:
Line L3:
Line L4: Parallelism: Lines are parallel if they have the same slope.
Here, . Thus, L1, L3, and L4 are parallel to each other.Perpendicularity: Lines are perpendicular if the product of their slopes is .
. Thus, L2 is perpendicular to L1.
Since L1, L3, and L4 are parallel, L2 is also perpendicular to L3 and L4.Evaluating the options:
(A) L1 is parallel to L2 (False, ).
(B) L2 is parallel to L4 (False, ).
(C) L3 is perpendicular to L4 (False, ).
(D) L4 is perpendicular to L2 (True, ) and L4 is parallel to L3 (True, ).Therefore, the correct option is (D).
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