Lesson 9: Perimeter and Area of Triangles in the Cartesian Plane
Parallel and perpendicular lines in the cartesian plane
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Transcript of Parallel and perpendicular lines in the cartesian plane
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Parallel and Perpendicular Lines in the
Cartesian Plane
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They are boring!
They have no use in life.
STEREOTYPES ABOUT PARALLEL AND PERPENDICULAR LINES
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Just a series of lines with positive slopes…
No Big Deal
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Color coded to show
parallel and
perpendicular lines
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WHOA!
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I know… I’m Awesome!
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PARALLEL AND PERPENDICULAR LINES ARE EVERYWHERE
Construction
Maps
Sports
Artwork
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y = mx + b m is the slope of the lineb is the y-intercept
REVIEW: SLOPE INTERCEPT FORM
Life is easy when you’re
in slope
intercept form
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y = mx + b
The y-intercept is the y value when x = 0.
Visually, the y-intercept is y value when the line crosses the y axis
http://www.mathsisfun.com/data/function-grapher.php
Y -INTERCEPT
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m
y = mx + bSlope Slider
Slope ofvertical lines?
SLOPE
(𝑥1 , 𝑦1)
(𝑥2 , 𝑦 2)
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3y = 6x + 9
5y = 10x
y = -1
x = 3
IDENTIFYING THE SLOPE AND THE Y-INTERCEPT
Hint
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y = mx + bGiven the slope, m, and a point, (x , y),
then we can find b, the y-intercept.
b = y – mxOnce we find b, we can find the equation of the
line.
REVIEW: FINDING THE EQUATION OF THE LINE GIVEN A SLOPE AND A POINT ON THE LINE
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p = (-2 , 2) m = 4
p = (-3 , 4) m = -2
p = (-2 , 2/3) m = -4/3
PRACTICE: FINDING THE EQUATION OF THE LINE GIVEN THE SLOPE AND A POINT ON THE LINE
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1. Graph line segments. Be sure that each endpoint is an integer coordinate, such as (1,3) or (-3,0)Compute and record their slope.
2. Then graph a parallel line to each of the three line segments. Compute and record the slopes of the parallel lines. Then delete the parallel lines.
3. Then graph a perpendicular line to each of the three line segments. Compute and record the slopes of the perpendicular lines.
GRAPHING ACTIVITY
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PARALLEL LINES
Two lines are parallel
The lines never
intersect
Slopes are equal
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y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
4y = 8x
y = 6
x = -3
FIND THE SLOPE OF A PARALLEL LINE
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PERPENDICULAR LINES
Two lines are perpendicular
The lines intersect at right angle
Slopes are negative
reciprocals
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y = -3x – 2
y = (1/3)x + 2
y – 1 = 6x
2y = 5x + 3
y = 6
x = -3
FIND THE SLOPE OF A PERPENDICULAR LINE
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y = (1/3)x + 2 , p = (2 , -3)
2y = 5x + 3 , p = (1/2 , 2/3)
y = 6 , p = (6 , 0)
x = -3 , p = (1 , 2)
FIND THE EQUATION OF THE PARALLEL LINE THAT PASSES THROUGH THE GIVEN POINT.
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y = -3x – 2 , p = (-1 , 4)
4y = 8x , p = (1 , 1/3)
y = 6 , p = (6 , 0)
x = -3 , p = (1 , 2)
FIND THE EQUATION OF THE PERPENDICULAR LINE THAT PASSES
THROUGH THE GIVEN POINT.