5-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation Pre-Algebra

5-5 Coordinate Geometry Warm Up Complete each sentence. Pre-Algebra 5-5 Coordinate Geometry Warm Up Complete each sentence. 1. Two lines in a plane that never meet are called lines. 2. lines intersect at right angles. 3. The symbol || means that lines are . 4. When a transversal intersects two lines, all of the acute angles are congruent. parallel Perpendicular parallel parallel

Problem of the Day What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

Learning Goal Assignment Learn to identify polygons in the coordinate plane.

Vocabulary slope rise run

In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies. Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

Slope is a number that describes how steep a line is.

vertical change horizontal change rise run slope = = The slope of a horizontal line is 0. The slope of a vertical line is undefined.

Additional Example 1A: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A. XY positive slope; slope of XY = = –5 –4 5 4

Additional Example 1B: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B. ZA negative slope; slope of ZA = = – –1 2 1

Additional Example 1C: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. C. BC slope of BC is undefined

Additional Example 1D: Finding the Slope of a Line Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. D. DM slope of DM = 0

Try This: Example 1A Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A A. AB positive slope; slope of AB = 1 8 C E F G H D

Try This: Example 1B Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A B. CD slope of CD is undefined C E F G H D

Try This: Example 1C Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A C. EF slope of EF = 0 C E F G H D

Try This: Example 1D Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. B A D. GH negative slope; slope of GH = = – –1 3 1 C E F G H D

Slopes of Parallel and Perpendicular Lines Two lines with equal slopes are parallel. Two lines whose slopes have a product of –1 are perpendicular.

Additional Example 2: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular? slope of EF = 3 2 slope of GH = 3 5 slope of PQ = 3 5 2 3 slope of CD = or – –2 slope of QR = or –1 3 –3

Additional Example 2 Continued Which lines are parallel? Which lines are perpendicular? GH || PQ The slopes are equal. = 3 5 EF  CD The slopes have a product of –1: • – = –1 3 2

Which lines are parallel? Which lines are perpendicular? Try This: Example 2 Which lines are parallel? Which lines are perpendicular? slope of AB = or –6 4 –3 2 slope of CD = –2 3 A slope of EF = or –4 6 –2 3 C K D E slope of GH = 2 3 H J B slope of JK = or 1 3 G F

Try This: Example 2 Continued Which lines are parallel? Which lines are perpendicular? CD || EF The slopes are equal. = –2 3 A C K D GH  AB E H The slopes have a product of –1: • – = –1 2 3 J B G F

Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP Lesson Quiz Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? 1 – 10 3 8 7 MN, RQ