1. Pre-Algebra 5.5 Coordinate Geometry

2. 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 Warm Up

3. Learn to identify polygons in the coordinate plane.

4. slope rise run Vocabulary

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

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

7. 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 5454 Example: Finding the Slope of a Line

8. 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 1212 Example: Finding the Slope of a Line

9. 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 Example: Finding the Slope of a Line

10. 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 Example: Finding the Slope of a Line

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

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

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

14. D. GH Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. A C B D F E H G negative slope; slope of GH = = – –1 3 1313 Try This

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

16. Which lines are parallel? Which lines are perpendicular? slope of EF = 3232 slope of GH = 3535 slope of PQ = 3535 slope of QR = or –1 3 –3 2323 slope of CD = or – –2 3 Example: Finding Perpendicular Line and Parallel Lines

17. The slopes are equal. = 3535 3535 The slopes have a product of –1: – = –1 3232 2323 GH || PQ EF  CD Which lines are parallel? Which lines are perpendicular? Example Continued

18. A C B D F E K J H G Which lines are parallel? Which lines are perpendicular? slope of AB = or –6 4 –3 2 slope of CD = –2 3 slope of EF = or –4 6 –2 3 slope of GH = 2323 slope of JK = or 1 3 Try This

19. CD || EF GH  AB A C B D F E K J H G Which lines are parallel? Which lines are perpendicular? The slopes are equal. = –2 3 –2 3 The slopes have a product of –1: – = –1 2323 3232 Try This

20. 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 CD || BA and BC || AD Example: Using Coordinates to Classify Quadrilaterals

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

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

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

24. 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) parallelogram A C B D CD || BA and BC || AD Try This

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

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

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

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

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

30. 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) parallelogram A C B D CD || BA and BC || AD Try This

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

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

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

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