Plane $ P $ contains four distinct lines $ l_1, l_2, l_3, $ and $ l_4 $. Suppose $ l_1 \parallel l_2 $, $ l_3 \parallel l_4 $, and $ l_1 \perp l_3 $.

How are $ l_1 $ and $ l_4 $ related? Choose the correct answer below.

A. $ l_4 $ is perpendicular to $ l_1 $, because $ l_1 $ is parallel to $ l_2 $ and $ l_3 $ is parallel to $ l_4 $.

B. $ l_4 $ is parallel to $ l_1 $, because $ l_1 $ is perpendicular to $ l_3 $ and $ l_3 $ is parallel to $ l_4 $.

C. $ l_4 $ is perpendicular to $ l_1 $, because $ l_1 $ is perpendicular to $ l_2 $ and $ l_2 $ is parallel to $ l_3 $.

D. $ l_4 $ is parallel to $ l_1 $, because $ l_1 $ is parallel to $ l_2 $ and $ l_2 $ is parallel to $ l_4 $.

Question

30-12-2024
Mathematics

High School

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Plane $ P $ contains four distinct lines $ l_1, l_2, l_3, $ and $ l_4 $. Suppose $ l_1 \parallel l_2 $, $ l_3 \parallel l_4 $, and $ l_1 \perp l_3 $.

How are $ l_1 $ and $ l_4 $ related? Choose the correct answer below.

A. $ l_4 $ is perpendicular to $ l_1 $, because $ l_1 $ is parallel to $ l_2 $ and $ l_3 $ is parallel to $ l_4 $.

B. $ l_4 $ is parallel to $ l_1 $, because $ l_1 $ is perpendicular to $ l_3 $ and $ l_3 $ is parallel to $ l_4 $.

C. $ l_4 $ is perpendicular to $ l_1 $, because $ l_1 $ is perpendicular to $ l_2 $ and $ l_2 $ is parallel to $ l_3 $.

D. $ l_4 $ is parallel to $ l_1 $, because $ l_1 $ is parallel to $ l_2 $ and $ l_2 $ is parallel to $ l_4 $.

Answer :

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nithishkumar12se nithishkumar12se · Answer 1 · 2024-02-11T13:20:48-05:00

Final answer:

Without more specific information from the question, it's generally understood that lines in a plane can be parallel, perpendicular, or neither. If two lines are both perpendicular to a third line, then they are parallel to each other.

Explanation:

From the given problem statement, it's unclear as the question appears to contain several typographical errors, making it difficult to determine the relationships between the mentioned lines. However, I can provide you some general understandings of distinct lines in a plane.

In geometry, lines in a plane can have one of three relations: they can be parallel, perpendicular, or neither. Parallel lines are lines in the same plane that never intersect. Perpendicular lines intersect at a 90-degree angle. If two lines are both perpendicular to a third line, then they are parallel to each other.

Unfortunately, with the provided information, we can't determine whether line 4 is parallel or perpendicular to the other lines because we don't know their orientations.

Learn more about Lines in a Plane here:

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