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

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, [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.