Unit 3 Day 4 Notes Parallel and Perpendicular Lines...
Transcript of Unit 3 Day 4 Notes Parallel and Perpendicular Lines...
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:
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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.