Geometry Notes Lesson 1.2b Equations of parallel, perpendicular lines and perpendicular bisectors...
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Transcript of Geometry Notes Lesson 1.2b Equations of parallel, perpendicular lines and perpendicular bisectors...
Geometry Notes Lesson 1.2b
Equations of parallel, perpendicular lines and perpendicular bisectors
CGT.5.G.2 Write equations of lines in slope-intercept form and use slope to determine
parallel and perpendicular lines.
Review
□Slope-intercept form of a line:
□Slope of a line:
y = mx + b
m = 12
12
xx
yy
Example
□What is the slope and y-intercept of the line y = ¾ x – 5?
M = ¾ b = -5
General form of a line
Ax + By = C
Review
Example: □Write the equation 3x – 7y = 14 in
slope-intercept form.
Review
Parallel lines Review
□The slope of two parallel lines is always
□What is the slope of the line parallel to y = -½ x +2?
□What is the slope of the line parallel to 2x + 10y = 20?
the same
-1/2
-1/5
Writing Equations Example #1
□Write the equation of the line parallel to 7x – 8y = 16 that goes through the point (-8, 3).
Two methods: □Slope-Intercept Method□Point-Slope Method
thru (-8, 3) Parallel to 7x – 8y = 16
y = mx + b
Method 1: Slope - Intercept
thru (-8, 3) Parallel to 7x – 8y = 16
y-y1 = m(x-x1)
Method 2: Point - Slope
Now You Try…
□Write the equation of the line parallel to the given line through the given point: 11x + 5y = 55 ; (-5, 12)
Y = -11/5x + 1
Perpendicular Lines
□What are perpendicular lines?
□The slopes of perpendicular lines are always
□What is the slope of the line perpendicular to y = 2/3 x - 4?
two lines that intersect at a right angle
Opposite reciprocals
-3/2
Example #2:
□Write the equation of the line perpendicular to y = -8/9 x – 2 through the point (8, 3).
thru (8, 3) Perp. to y = -8/9 x – 2
y = mx + b
Method 1: Slope - Intercept
Method 2: Point - Slope
thru (8, 3) Perp. to y = -8/9 x – 2
y-y1 = m(x-x1)
Now You Try…
□Write the equation of the line perpendicular to the given line through the given point. y = 3/7 x – 1 ; (3, -10)
Y = -7/3x - 3
Perpendicular Bisectors
□What is a perpendicular bisector? □a line or segment that is
perpendicular to a segment and intersects it at its midpoint
Steps for finding the Perpendicular Bisector of a
Segment 1. Find the midpoint of the
segment2. Find the slope of the segment3. Find the Perpendicular slope4. Write the equation using either
Point-Slope or Slope-Intercept methods
Example #3:
□Write the equation of the perpendicular bisector of the segment with the two given endpoints: (1, 0) and (-5, 4)
Now You Try…
□Write the equation of the perpendicular bisector of the segment with the two given endpoints: (-2, -12) and (-8, -2)
Y = 3/5x - 4