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Understanding Coordinate Geometry: Lines, Slope, and Quadrilaterals

This presentation covers key concepts in coordinate geometry, including the definitions and properties of parallel and perpendicular lines, slope calculations, and identifying different types of polygons such as parallelograms, rectangles, and rhombuses. Students will learn how to classify quadrilaterals using their coordinates and understand how the slope can indicate line relationships. This essential lesson is designed to enhance students' understanding of geometric concepts and their practical applications in various fields such as computer graphics.

barrett-kennedy
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Understanding Coordinate Geometry: Lines, Slope, and Quadrilaterals

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  1. 5-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  2. 5-5 Coordinate Geometry Pre-Algebra 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

  3. 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

  4. Learn to identify polygons in the coordinate plane.

  5. Vocabulary slope rise run

  6. 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.

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

  8. riserun vertical change horizontal change = slope = The slope of a horizontal line is 0. The slope of a vertical line is undefined.

  9. A. XY positive slope; slope of XY = = 5 4 –5 –4 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.

  10. negative slope; slope of ZA = = – –1 2 1 2 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

  11. slope of BC is undefined 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

  12. slope of DM = 0 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

  13. A. AB positive slope; slope of AB = 1 8 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 C E F G H D

  14. slope of CD is undefined 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 C E F G H D

  15. slope of EF = 0 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 C E F G H D

  16. negative slope; slope of GH = = – –1 3 1 3 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 C E F G H D

  17. 3 2 slope of EF = 3 5 slope of GH = 3 5 slope of PQ = –2 3 2 3 slope of CD = or – 3 –3 slope of QR = or –1 Additional Example 2: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular?

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

  19. –4 6 –6 4 –2 3 –3 2 slope of EF = or slope of AB = or –2 3 slope of CD = 2 3 slope of GH = 3 3 slope of JK = or 1 Try This: Example 2 Which lines are parallel? Which lines are perpendicular? A C K D E H B J G F

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

  21. CD || BA and BC || AD Additional Example 3A: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(3, –2), B(2, –1), C(4, 3), D(5, 2) parallelogram

  22. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Additional Example 3B: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2) parallelogram, rectangle, rhombus, square

  23. GH || JI Additional Example 3C: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. G(1, –1), H(1, –2), I(3, –3), J(3, 1) trapezoid

  24. WZ || XY and WX || ZY WZ^ZY, ZY^XY, XY^WX and WX^WZ Additional Example 3D: Using Coordinates to Classify Quadrilaterals Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0) parallelogram, rectangle

  25. CD || BA and BC || AD Try This: Example 3A Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3) B C A D parallelogram

  26. EF || HG Try This: Example 3B Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. B. E(1, 5), F(7, 5), G(6, 1), H(2, 1) E F trapezoid G H

  27. ZW || YX and WX || ZY WX^ZW, XY^WX, YZ^XY and ZW^YZ Try This: Example 3C Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4) W Z X parallelogram, rectangle, rhombus, square Y

  28. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Try This: Example 3D Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral. D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1) S T R parallelogram, rectangle U

  29. 10 3 – MN, RQ Lesson Quiz Determine the slope of each line. 1.PQ 2.MN 3.MQ 4.NP 5. Which pair of lines are parallel? 1 8 7

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