Maintaining Mathematical Proficiency Worksheet

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Presentation transcript:

Maintaining Mathematical Proficiency Worksheet Daily Warm Up Maintaining Mathematical Proficiency Worksheet

Equations of Parallel & Perpendicular Lines Notes 3.5 Goals: Use slope to partition directed line segments Identify parallel & perpendicular lines Write equations of parallel & perpendicular lines Use slope to find the distance from a point to a line.

Partitioning a Line Segment Example 1. Partitioning a Line Segment Find the coordinates of point P along the directed line segment AB so that the ratios of AP to PB is 3 to 2. Ask students “what words are you not sure, or do no understand, in this question?” DO NOT DO THIS PROBLEM! GO TO NEXT SLIDE

A segment that represents moving from point A to point B. Core Vocabulary Directed Line Segment A segment that represents moving from point A to point B. Simply put…in my own words Directed Line Segment AB means start at point A and trace the line ending at point B

Partitioning a Line Segment Example 1. Partitioning a Line Segment Find the coordinates of point P along the directed line segment AB so that the ratios of AP to PB is 3 to 2.

Core Concept Slopes of Parallel Lines Theorem 3.13 In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. any two vertical lines are parallel Given: So by the slopes of parallel lines theorem we can conclude…

Core Concept Slopes of Perpendicular Lines Theorem 3.13 In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is –1. a horizontal line & a vertical line are always perpendicular Given: So by the slopes of parallel lines theorem we can conclude…

Identifying Parallel & Perpendicular Lines Example 2. Identifying Parallel & Perpendicular Lines Determine which of the lines are parallel & which of the lines are perpendicular.

Writing an Equation of a Parallel Line Example 3. Writing an Equation of a Parallel Line Write an equation of the line passing through the point (–1, 1) that is parallel to the line y = 2x – 3

Writing an Equation of a Perpendicular Line Example 4. Writing an Equation of a Perpendicular Line Write an equation of the line passing through the point (2,3) that is perpendicular to the line 2x + y = 2

Finding the Distance from a Point to a Line Example 5. Finding the Distance from a Point to a Line Find the distance from the point (1,0) to the line y = –x + 3.

Practice Extra Practice – In Class Worksheet Hw #18– Big Ideas TB Pg. 1, 2, 3-7 odd, 8, 12-24 even, 30, 43

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