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Coordinate Geometry

Coordinate Geometry. 5.5. 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 .

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Coordinate Geometry

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  1. Coordinate Geometry 5.5 Pre-Algebra

  2. 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. Learn to identify polygons in the coordinate plane.

  4. Vocabulary slope rise run

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

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

  7. A. XY positive slope; slope of XY = = 5 4 –5 –4 Example: 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.

  8. negative slope; slope of ZA = = – –1 2 1 2 Example: 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

  9. slope of BC is undefined Example: 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

  10. slope of DM = 0 Example: 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

  11. A. AB positive slope; slope of AB = 1 8 Try This 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

  12. slope of CD is undefined Try This 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

  13. slope of EF = 0 Try This 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

  14. negative slope; slope of GH = = – –1 3 1 3 Try This 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

  15. 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 Example: Finding Perpendicular Line and Parallel Lines Which lines are parallel? Which lines are perpendicular?

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

  17. –4 6 –6 4 –2 3 –3 2 slope of AB = or slope of EF = or –2 3 slope of CD = 2 3 slope of GH = 3 3 slope of JK = or 1 Try This Which lines are parallel? Which lines are perpendicular? A C K D E H B J G F

  18. 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 Which lines are parallel? Which lines are perpendicular? A C K D E H B J G F

  19. CD || BA and BC || AD Example: 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

  20. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Example: 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

  21. GH || JI Example: 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

  22. WZ || XY and WX || ZY WZ^ZY, ZY^XY, XY^WX and WX^WZ Example: 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

  23. CD || BA and BC || AD Try This 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

  24. EF || HG Try This 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

  25. ZW || YX and WX || ZY WX^ZW, XY^WX, YZ^XY and ZW^YZ Try This 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

  26. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Try This 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

  27. 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

  28. WZ || XY and WX || ZY WZ^ZY, ZY^XY, XY^WX and WX^WZ Example: 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

  29. CD || BA and BC || AD Try This 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

  30. EF || HG Try This 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

  31. ZW || YX and WX || ZY WX^ZW, XY^WX, YZ^XY and ZW^YZ Try This 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

  32. TU || SR and ST || RU TU^RU, RU^RS, RS^ST and ST^TU Try This 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

  33. 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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