Parallel And Perpendicular Lines Worksheet With Answer Key

Parallel And Perpendicular Lines Worksheet With Answer Key - Mausmi Jadhav Page 7

Solution to Q1:

The slope of the line is given by

m = ( 5 - 1 ) / (4 - 2) = 4 / 2 = 2

Since the slope is positive, the line rises as x increases.

The slope of the line is given by

m = ( -5 - 0 ) / ( 3 - (-1) ) = -5 / 4

Since the slope is negative, the line falls as x increases.

We first find the slope of the line

m = ( 1 - 1 ) / ( -3 - 2 ) = 0

Since the slope is equal to zero, the line is horizontal (parallel to the x axis).

The slope of the line is given by

m = ( -5 - 2 ) / ( -1 - (-1) )

Since ( -1 - (-1) ) = 0 and the division by 0 is not defined, the slope of the line is undefined

and the line is vertical. (parallel to the y axis).

Solution to Q5:

In what follows, m1 is the slope of line L1 and m2 is the slope of line L2.

Find the slope m1 of line L1 and the slope m2 of line L1

m1 = ( 1 - 2 ) / ( 3 - 1 ) = -1 / 2

m2 = ( 0 - (-1) ) / ( 2 - 0 ) = 1/2

The two slopes m1 and m2 are not equal and their products is not equal to -1. Hence the

two lines are neither parallel nor perpendicular.

b. m1 = ( 1 - 3 ) / ( 3 - 0 ) = -2 / 3

m2 = ( -5 - 4 ) / ( -7 - (-1) ) = -9 / -6 = 3/2

The product of the two slopes m1*m2 = (-2 / 3)(3 / 2) = -1, the two lines are

perpendicular.

c. m1 = ( -7 - (-1) ) / ( 5 - 2 ) = -6 / 3 = -2

m2 = ( 2 - 0 ) / ( -1 - 0 ) = -2

The two slopes are equal, the two lines are parallel.

d. m1 = ( 0 - 0 ) / ( 2 - 1 ) = 0 / 1 = 0

m2 = ( -5 - (-5) ) / ( -10 - 5 ) = 0 / -15 = 0

The two slopes are equal , the two lines are parallel. Also the two lines are horizontal

e. m1 = ( 7 - 5 ) / ( -2 - (-2) )

m2 = ( 13 - 1 ) / ( 5 - 5 )

The two slopes are both undefined since the denominators in both m1 and m2 are equal

to zero. The two lines are vertical lines and therefore parallel.

Solution to Q6:

No. If both slopes are negative, their product can never be equal to -1.

Note: This worksheet is supported by a flash presentation, under Mausmi’s Math Movies.

Mausmi Jadhav

Parallel And Perpendicular Lines Worksheet With Answer Key - Mausmi Jadhav Page 7