WORK PROGRAM

Chapter 5 Coordinate geometry

Strands: Patterns and algebra, Measurement

Substrands and outcomes:

Perimeter and area MS4.1Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figurescomposed

of rectangles and triangles

Algebraic techniquesPAS4.4 Use algebraic techniques to solve linear equations and simple inequalities

Linear relationshipsPAS4.5Graphs and interprets linear relationships on the number plane

Coordinate geometryPAS5.1.2Determines the midpoint, length and gradient of an interval joining two points on the number planeand

graphs linear and simple non-linear relationships from equations

Coordinate geometryPAS5.2.3Uses formulae to find midpoint, distance and gradient and applies the gradient/intercept form tointerpret

and graph straight lines

Coordinate geometryPAS5.3.3Uses various standard forms of the equation of a straight line and graphs regions on the number plane

Section / GC tips, Investigations,
History of mathematics, Maths Quest challenge, 10 Quick Questions,
Code puzzles,
Career profiles / SkillSHEETs, WorkSHEETs, Interactive games, Testyourself, Topic tests
(CD-ROM) / Technology applications
(CD-ROM) / Learning outcomes

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Are you ready? (page 182) / SkillSHEETs (page230)
5.1: Measuring the rise and run
5.3: Describing the gradient of a line
5.4: Plotting a line using a table of values
5.5: Stating the y-intercept from a graph
5.7: Solving linear equations that arise when finding x- and y-intercepts
5.10: Using Pythagoras’ theorem / PAS5.1.2
  • using the right-angled triangle drawn between two points on the number plane and the relationship gradient=to find the gradient of the interval joining two points
  • determining whether a line has a positive or negative slope by following the line from left to right – if the line goes up it has a positive slope and if it goes down it has a negative slope
  • identifying the y-intercept of a graph
PAS4.5
  • forming a table of values for a linear relationship by substituting a set of appropriate values for either of the letters and graphing the number pairs on the number plane
PAS4.4
  • solving equations arising from substitution into formulae
MS4.1
  • using Pythagoras’ theorem to find the length of sides in right-angled triangles

Gradient of a straight line (page 183)
WE 1, 2
Ex 5A Gradient of a straight line (page 184) / SkillSHEET 5.1: Measuring the rise and run (page 184)
SkillSHEET 5.2: Finding the gradient given two points (page 185)
SkillSHEET 5.3: Describing the gradient of a line (page 187) / Mathcad:Gradient of a straight line (page 184)
Excel:Gradient of a straight line (page 184)
GC program Casio: Gradient of a straight line (page 185)
GC program  TI: Gradient of a straight line (page 185)
Cabri geometry:Gradient of a straight line (page185) / PAS5.1.2
  • using the right-angled triangle drawn between two points on the number plane and the relationship
    gradient=
    to find the gradient of the interval joining two points
  • determining whether a line has a positive or negative slope by following the line from left to right  if the line goes up it has a positive slope and if it goes down it has a negative slope
  • finding the gradient of a straight line from the graph by drawing a right-angled triangle after joining two points on the line
  • distinguishing between positive and negative gradients from a graph (Communicating)
PAS5.2.3
  • using the relationship
    gradient=
    to establish the formula for the gradient, m, of an interval joining two points (x1, y1) and (x2,y2) on the number plane
  • using the formula to find the gradient of an interval joining two points on the number plane
  • explaining the meaning of each of the pronumerals in the formula for gradient (Communicating)
  • using the appropriate formulae to solve problems on the number plane (Applying strategies)

Equations of the form y=mx+b (page 188)
WE 3
Ex 5B Equations of the form y = mx + b (page189) / Investigation:Relating equations and graphs to values of gradients and intercepts (page 191) / SkillSHEET 5.4: Plotting a line using a table of values (page 189)
SkillSHEET 5.5: Stating the y-intercept from a graph (page 189)
SkillSHEET 5.6: Finding the gradient of a line from its equation (page192)
WorkSHEET 5.1 (page190) / Mathcad:Linear graphs (page 189)
Excel:Linear graphs (page189)
GC program Casio: Guess the equation (page190)
GC program  TI:Guess the equation (page 190) / PAS5.2.3
  • recognising equations of the form y=mx+b as representing straight lines and interpreting the x-coefficient (m) as the gradient and the constant (b) as the y-intercept
  • determining that two lines are parallel if their gradients are equal
  • finding the gradient and y-intercept of a straight line from the graph and using them to determine the equation of the line
  • comparing similarities and differences between sets of linear relationships (Reasoning)
  • explaining the effect on the graph of a line of changing the gradient or y-intercept (Reasoning, Communicating)
  • using a graphics calculator and spreadsheet software to graph a variety of equations of straight lines, and compare and describe the similarities and differences between the lines (Applying strategies, Communicating, Reasoning)

Sketching linear graphs (page 193)
WE 4, 5
Ex 5C Sketching linear graphs (page 195) / GC tip  Casio:Finding the x- and y-intercepts (page 196)
10 Quick Questions 1 (page 196)
Code puzzle (page 197) / SkillSHEET 5.7: Solving linear equations that arise when finding x- and
y-intercepts (page 195)
SkillSHEET 5.8: Graphing linear equations using the x- and y-intercept method (page 195)
Game time 001(page 195) / GC tip  TI:Finding the x- and y-intercepts (page196)
Excel:Linear graphs (page195)
Cabri geometry: Gradient of a straight line (page195) / PAS5.1.2
  • identifying the x- and y-intercepts of graphs
PAS5.2.3
  • graphing equations of the form y = mx + b using the y-intercept(b) and the gradient (m)
  • rearranging an equation in general form (ax + by + c = 0) to the gradientintercept form
PAS5.3.3
  • describing the equation of a line as the relationship between the x- and y-coordinates of any point on the line
  • sketching the graph of a line by finding the x- and y-intercepts from its equation

Perpendicular lines (page198)
WE 6
Ex 5D Perpendicular lines (page 199) / Investigation:Pairs of perpendicular lines (page198) / Excel:Perpendicular checker (page 199)
GC tip  TI: Viewing perpendicular lines (page199) / PAS5.2.3
  • using the formula to find the gradient of an interval joining two points on the number plane
PAS5.3.3
  • demonstrating that two lines are perpendicular if the product of their gradients is –1
  • describing conditions for lines to be perpendicular (Reasoning, Communicating)
  • showing that if two lines are perpendicular then the product of their gradients is −1 (Applying strategies, Reasoning, Communicating)

Formula for finding the equation of a straight line (page 200)
WE 7, 8
Ex 5E Formula for finding the equation of a straight line (page 202) / Investigation:Which phone company is cheaper? (page 203) / Game time 002 (page 202)
WorkSHEET 5.2 (page202) / Mathcad:Equation of a straight line (page 202)
Excel: Equation of a straight line (page 202)
GC program Casio: Equation of straight line (page 202)
GC program TI: Equation of straight line (page 202) / PAS5.3.3
  • finding the equation of a line passing through a point (x1, y1), with a given gradient m, using:
y – y1 = m(x – x1)
y = mx + b
  • finding the equation of a line passing through two points
  • recognising and finding the equation of a line in the general form: ax+by+c=0
  • finding the equation of a line that is parallel or perpendicular to a given line
PAS5.2.3
  • finding the gradient and y-intercept of a straight line from the graph and using them to determine the equation of the line

Graphs of linear inequalities (page 204)
WE 9, 10, 11, 12
Ex 5F Graphs of linear inequalities (page 207) / 10 Quick Questions 2 (page 209) / SkillSHEET 5.9: Checking whether a given point makes the inequality a true statement (page 207) / Mathcad:Horizontal and vertical graphs (page207)
Graphmatica (page 208)
GrafEq (page 208) / PAS5.3.3
  • graphing inequalities of the form ya, ya, ya, ya, xa, xa, xa and xa
on the number plane
  • graphing inequalities such as yxon the number plane by considering the position of the boundary of the region as the limiting case
  • checking whether a particular point lies in a given region specified by a linear inequality
  • graphing regions such as that specified by x+y7, 2x3y5

Distance between two points (page 209)
WE 13
Ex 5G Distance between two points (page 210) / SkillSHEET 5.10: Using Pythagoras’ theorem (page 210) / Mathcad:Distance between two points (page210)
Excel: Distance between two points (page 210)
GC program Casio: Distance between two points (page210)
GC program TI: Distance between two points (page210)
Cabri geometry: Distance between two points (page210) / PAS5.2.3
  • using Pythagoras’ theorem to establish the formula for distance, d, between two points () and () on the number plane
  • using the formula to find the distance between two points on the number plane
  • using the appropriate formulae to solve problems on the number plane (Applying strategies)

Midpoint of a segment (page 212)
WE 14, 15
Ex 5H Midpoint of a segment (page 213) / Investigation:A Romanaqueduct (page 262) / WorkSHEET 5.3 (page213) / Mathcad: Midpoint of a segment (page 213)
Excel: Midpoint of a segment (page 213)
GC programCasio: Midpoint of a segment (page 213)
GC program TI: Midpoint of a segment (page 213)
Cabri geometry: Midpoint of a segment (page 213) / PAS5.2.3
  • using the average concept to establish the formula for the midpoint, M, of the interval joining two points () and () on the number plane
  • using the formula to find the midpoint of the interval joining two points on the number plane
  • using the appropriate formulae to solve problems on the number plane (Applying strategies)
  • applying the knowledge and skills of linear relationships to practical problems (Applying strategies)

Summary (page 214)
Chapter review (page 215) / ‘Test yourself’ multiple choice questions
Topic tests (2)

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