Math 10C Module 6: Lesson 3

Module 6: Linear Equations

Lesson 3: Parallel and Perpendicular Lines

Focus

This shows a chair against a background featuring a Piet Mondrian design. The design consists of parallel and perpendicular lines mixed with coloured rectangles.

© aA./12578997/Fotolia

Piet Mondrian was a painter who lived in the early 1900s. Painting was his recreational pastime while he worked as a primary school teacher. Later, he would become famous for his artwork, particularly those he classified as Neo-Plasticism. Art in this style can be seen in the photo, where an irregular grid of parallel and perpendicular lines is painted on a white background. Some of the spaces in between are painted with the primary colours. Today, you can see this type of design in clothing, shoes, and stained glass artwork.

You have previously learned the definitions of parallel and perpendicular lines. In this lesson you will learn how the slopes of lines can be used to identify whether a set of lines is parallel, perpendicular, or neither. You will also learn how to determine the equations of lines that are either parallel or perpendicular to other lines. At the end of this lesson, you will have the opportunity to select and analyze a work of art for parallel and perpendicular lines.

Outcomes

At the end of this lesson, you will be able to

  • generalize and apply a rule for determining whether two lines are parallel or perpendicular

  • write the equation of a linear relation given the coordinates of a point on the line and the equation of a parallel or perpendicular line, and explain the reasoning

Lesson Questions

  • How can you determine the relative orientation of a pair of lines by examining their slopes?

  • How can knowledge of mathematical relationships between parallel and perpendicular lines be applied to problem-solving situations?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Activities block on the left in moodle or under the Assess tab.


** Note – Share questions may have to be done on your own depending on your learning situation**