UH MATH 1300 - Chapter 2 Points, Lines, and Functions

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Chapter 2Points, Lines, and FunctionsSection 2.1: An Introduction to the Coordinate PlanePoints in the Coordinate PlanePlot the following points in a coordinate plane.Section 2.2: The Distance and Midpoint FormulasThe Distance FormulaThe Midpoint FormulaUse the Pythagorean Theorem to find the missing side of each of the following triangles.Section 2.3: Slope and Intercepts of LinesThe Slope of a LineIntercepts of LinesState whether the slope of each of the following lines is positive, negative, zero, or undefined.Section 2.4: Equations of LinesWriting Equations of LinesWrite an equation in slope-intercept form for each of the following lines.Section 2.5: Parallel and Perpendicular LinesPairs of Lines - Parallel and Perpendicular LinesState whether the following pairs of lines are parallel, perpendicular, or neither.Section 2.6: An Introduction to FunctionsDefinition of a FunctionDomain of a FunctionState whether or not each of the following mappings represents a function.Section 2.7: Functions and GraphsGraphing a FunctionDetermine whether or not each of the following graphs represents a function.CHAPTER 2 Points, Lines, and FunctionsChapter 2 Points, Lines, and FunctionsSection 2.1: An Introduction to the Coordinate Plane Points in the Coordinate PlanePoints in the Coordinate Plane The Rectangular Coordinate System: University of Houston Department of Mathematics104CHAPTER 2 Points, Lines, and FunctionsUniversity of Houston Department of Mathematics105SECTION 2.1 An Introduction to the Coordinate PlanePlotting Points in the Coordinate Plane: MATH 1300 Fundamentals of Mathematics106CHAPTER 2 Points, Lines, and FunctionsExample: Solution: University of Houston Department of Mathematics107SECTION 2.1 An Introduction to the Coordinate PlaneGraphing Horizontal and Vertical Lines: Example: Solution: MATH 1300 Fundamentals of Mathematics108CHAPTER 2 Points, Lines, and FunctionsGraphing Other Lines: Example: Solution: University of Houston Department of Mathematics109SECTION 2.1 An Introduction to the Coordinate PlaneAdditional Example 1:Solution:MATH 1300 Fundamentals of Mathematics110CHAPTER 2 Points, Lines, and FunctionsAdditional Example 2: University of Houston Department of Mathematics111SECTION 2.1 An Introduction to the Coordinate PlaneSolution: Additional Example 3: MATH 1300 Fundamentals of Mathematics112CHAPTER 2 Points, Lines, and FunctionsSolution: Additional Example 4: Solution: University of Houston Department of Mathematics113SECTION 2.1 An Introduction to the Coordinate Plane (c) Draw a line through the points. MATH 1300 Fundamentals of Mathematics114CHAPTER 2 Points, Lines, and FunctionsAdditional Example 5: Solution: University of Houston Department of Mathematics115SECTION 2.1 An Introduction to the Coordinate PlaneMATH 1300 Fundamentals of Mathematics116CHAPTER 2 Points, Lines, and FunctionsUniversity of Houston Department of Mathematics117Exercise Set 2.1: An Introduction to the Coordinate PlanePlot the following points in a coordinate plane.1. A(3, 4)2. B(2, -5)3. C(-3, -1)4. D(-4, -6) 5. E(-5, 0)6. F(0, -2) Write the coordinates of each of the points shown in the figure below. Then identify the quadrant or axis inwhich the point is located.7. G8. H9. I10. J11. K12. LPlot each of the following sets of points in a coordinate plane. Then identify the quadrant or axis in which each point is located.13. (a) A(2, 5)(b) B(-2, -5)(c) C(2, -5)(d) D(-2, 5)14. (a) A(4, -3)(b) B(-4, -3)(c) C(-4, 3)(d) D(4, 3)15. (a) A(0, -2)(b) B(-2, 0)(c) C(2, 0)(d) D(0, 2)16. (a) A(-3, 0)(b) B(3, 0)(c) (0, -3)(d) D(0, 3)17. If the point (a, b) is in Quadrant I, identify the quadrant of each of the following points:(a) (-a, -b) (b) (-a, b) (c) (a, a)18. If the point (a, b) is in Quadrant I, identify the quadrant of each of the following points:(a) (-b, a) (b) (b, b) (c) (-b, -a)19. If the point (a, b) is in Quadrant II, then 0a < and 0b >. Identify the quadrant of each of the following points:(a) (-a, -b) (b) (b, a) (c) (a, -b)20. If the point (a, b) is in Quadrant III, then 0a < and 0b <. Identify the quadrant of each of the following points:(a) (-a, b) (b) (b, a) (c) (-a, -b)21. If the point (a, b) is in Quadrant IV, identify the quadrant of each of the following points:(a) (b, -b) (b) (-a, -a) (c) (b, a)22. If the point (a, b) is in Quadrant II, identify the quadrant of each of the following points:(a) (-a, b) (b) (b, b) (c) (a, -a)23. If the point (a, b) is in Quadrant III, identify the axis on which each of the following points lies:(a) (a, 0) (b) (0, b) (c) (-b, 0)24. If the point (a, b) is in Quadrant IV, identify the axis on which each of the following points lies:(a) (0, -b) (b) (-a, 0) (c) (b, 0)Answer True or False.25. The point (0, 5) is on the x-axis.26. The point (-4, 0) is in Quadrant II.27. The point (1, -3) is in Quadrant IV.28. The point (-2, -5) is in Quadrant III.29. The point (0, 0) is in Quadrant I.30. The point (-6, 1) is in Quadrant IV.31. If the point (a, b) is in Quadrant IV, then 0b <.32. If the point (a, b) is in Quadrant II, then 0a >.33. If the point (a, b) is in Quadrant I, then the point (b, a) is also in Quadrant I.MATH 1300 Fundamentals of Mathematics        xyHGIJKL118Exercise Set 2.1: An Introduction to the Coordinate Plane34. If the point (a, b) is in Quadrant I, then the point (a, -b) is in Quadrant II.35. If the point (a, b) is in Quadrant II, then the point(-a, -b) is in Quadrant III .36. If the point (a, b) is in Quadrant IV, then the point (-b, a) is in Quadrant I.37. If the point (a, b) is in Quadrant III, then 0b >.38. If the point (a, b) is on the y-axis, then 0a >.39. If the point (a, b) is on the y-axis, then 0b >.40. If the point (a, b) is on the y-axis, then 0a =.41. If the point (a, b) is on the y-axis, then the point (b, a) is on the x-axis.42. If the point (a, b) is on the x-axis, then the point (a, 3) lies in Quadrant I .Answer the following.43. Given the following points:A(3, 5), B(3, 1), C(3, 0), D(3, -2)(a) Plot the above points on a coordinate plane.(b) What do the above points have in common?(c) Draw a line through the above points.(d) What is the equation of the line drawn in part (c)?44. Given the following points:A(-3, 4), B(0, 4), C(1, 4), D(3, 4)(a) Plot the above points on a coordinate plane.(b) What do the above points have in common?(c) Draw a line through the above points.(d) What is the equation of the line drawn in part (c)?45. (a) List four


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UH MATH 1300 - Chapter 2 Points, Lines, and Functions

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