Equations of parallel, perpendicular lines and perpendicular bisectors

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Presentation transcript:

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 =

Example What is the slope and y-intercept of the line y = ¾ x – 5? M = ¾ b = -5

Review Ax + By = C General form of a line

Review Example: Write the equation 3x – 7y = 14 in slope-intercept form.

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

Method 1: Slope - Intercept thru (-8, 3) Parallel to 7x – 8y = 16 y = mx + b

Method 2: Point - Slope thru (-8, 3) Parallel to 7x – 8y = 16 y-y1 = m(x-x1)

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).

Method 1: Slope - Intercept thru (8, 3) Perp. to y = -8/9 x – 2 y = mx + b

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 Find the midpoint of the segment Find the slope of the segment Find the Perpendicular slope 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

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