Answer:
Two co planar lines that are perpendicular to the same line are always PARALLEL. So option A is correct.
Explanation:
Given:
- They are perpendicular to the same line
To find:
whether they are parallel or not and choose the correct option from the given options.
Solution:
Now, we know that, slopes of perpendicular lines is -1
Then, [tex]\text{{slope of 1st line}}\times \text{{slope of perpendicular line}} = -1[/tex]
[tex]\text{{slope of perpendicular line}} =\frac{- 1}{\text{{1st line slope}}}[/tex]
similarly
[tex]\text{{slope of 2st line}}\times \text{{slope of perpendicular line}} = -1[/tex]
[tex]\text{{slope of perpendicular line}} =\frac{- 1}{\text{{2st line slope}}}[/tex]
Now, as both lines are perpendicular to same line, then, we have to equate above both of them.
Then, [tex]\frac{- 1}{\text{{1st line slope}}}= \frac{-1 }{\text{{2nd line slope}}}[/tex]
1st line slope = 2nd line slope
Here, slopes of two lines are equal.
Hence, Two coplanar lines that are perpendicular to the same line are always parallel. So option A is correct.
