Question

two coplanar lines that are perpendicular to the same line are parallel. a) always b) sometimes c) never

Answer 1

Answer:

Two co planar lines that are perpendicular to the same line are always PARALLEL. So option A is correct.

Explanation:

Given:

• Two lines are coplanar.

• 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, $\text{{slope of 1st line}}\times \text{{slope of perpendicular line}} = -1$

$\text{{slope of perpendicular line}} =\frac{- 1}{\text{{1st line slope}}}$

similarly

$\text{{slope of 2st line}}\times \text{{slope of perpendicular line}} = -1$

$\text{{slope of perpendicular line}} =\frac{- 1}{\text{{2st line slope}}}$

Now, as both lines are perpendicular to same line, then, we have to equate above both of them.

Then, $\frac{- 1}{\text{{1st line slope}}}= \frac{-1 }{\text{{2nd line slope}}}$

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.