Parallel and Perpendicular LinesDefinitions

Perpendicular: Lines intersecting to form a right or 90o angle.

Reciprocal: The reciprocal of a fraction is the fraction where the numerator and denominator are switched.

Parallel Lines:

If two lines are parallel, they have the same slope.

If two distinct lines have the same slope, they are parallel.

Perpendicular Lines:

If two lines are perpendicular, the product of their slopes is -1. The slopes are negative reciprocals of each other.

If the slopes of two lines are negative reciprocals of each other, the line are perpendicular.

Unit 3 Day 4 Notes

Parallel and Perpendicular Lines

Definitions

Negative Reciprocal: A reciprocal where you also change the sign.

Example:

)

1) Find the negative reciprocal of 2.

2(Remember that 2 can be written as the fraction .1

Since the reciprocal is where we switch the numerator and denominator.

1The reciprocal of 2 is .2

Now, to make a negative reciprocalyou have to change the sign of the reciprocal.

1Since 2 is positive the negative reciprocal is - .2

Parallel and Perpendicular LinesExample:

For the line that runs through the two points (6, 3) and (4, 6) find the slope of a line parallel and the slope of a line perpendicular to the given line.

Parallel and Perpendicular LinesExample:

Determine if the following two lines are parallel, perpendicular or neither.

3y - x = 12 and y = -3x + 1

Parallel and Perpendicular Lines

On Your Own:

Find the slope of lines parallel and perpendicular to a line containing the following points.

1) (0, 5) and (-1, 6)

2) (-1, -5) and (3, -2)

Parallel and Perpendicular Lines

On Your Own Cont.:Determine if the following lines are parallel, perpendicular, or neither.

3) y = -2x + 3 and 6x + 3y = 9

4) y = 5x - 4 and 2x - 4y = 8

Parallel and Perpendicular Lines

Write the equation of the line that passes through point (2, 4) and is parallel to the line

.2 2y x �

Example:

Parallel and Perpendicular Lines

Write the equation of the line that passes through point (6, 5) and is perpendicular to the line -6x - 2y = 12.

Example:

Parallel and Perpendicular LinesOn Your Own:

1) Write the equation of the line that passes through point (2, -1) and parallel to the line

.8 2y x �

2) Write the equation of the line that passes through point (2, -1) and perpendicular to the line 2x - 9y = 5.