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WORK PROGRAM
Chapter 5 Coordinate geometry
Strands: Patterns and algebra, Measurement
Substrands and outcomes:
Perimeter and area
MS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures composed
of rectangles and triangles
Algebraic techniques
PAS4.4 Use algebraic techniques to solve linear equations and simple inequalities
Linear relationships
PAS4.5 Graphs and interprets linear relationships on the number plane
Coordinate geometry
PAS5.1.2 Determines the midpoint, length and gradient of an interval joining two points on the number plane and
graphs linear and simple non-linear relationships from equations
Coordinate geometry
PAS5.2.3 Uses formulae to find midpoint, distance and gradient and applies the gradient/intercept form to interpret
and graph straight lines
Coordinate geometry
PAS5.3.3 Uses various standard forms of the equation of a straight line and graphs regions on the number plane
Section
Are you ready? (page 182)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles
SkillSHEETs,
WorkSHEETs,
Interactive games,
Test yourself, Topic tests
(CD-ROM)
SkillSHEETs (page 230)
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 yintercepts
5.10: Using Pythagoras’
theorem
Technology applications
(CD-ROM)
Learning outcomes
PAS5.1.2
 using the right-angled
triangle drawn between
two points on the
number plane and the
relationship
rise
gradient = run to find
the gradient of the
interval joining two
points
 determining whether a
line has a positive or
negative slope by
1
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:
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 yintercept 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 rightangled triangles
Mathcad: Gradient of a
PAS5.1.2
straight line (page 184)
 using the right-angled
Excel: Gradient of a
triangle drawn between
straight line (page 184)
two points on the
number plane and the
GC program  Casio:
relationship
Gradient of a straight line
(page 185)
2
Describing the gradient
of a line (page 187)
GC program  TI:
Gradient of a straight line
(page 185)
Cabri geometry: Gradient
of a straight line
(page 185)

rise
gradient = run
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
rise
gradient = run
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
3
Equations of the form
y = mx + b (page 188)
WE 3
Ex 5B Equations of the
form y = mx + b
(page 189)
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
(page 192)
WorkSHEET 5.1
(page 190)
Mathcad: Linear graphs
(page 189)
Excel: Linear graphs
(page 189)
GC program  Casio:
Guess the equation
(page 190)
GC program  TI: Guess
the equation (page 190)
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)
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 yintercept
 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
4
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
GC tip  TI: Finding the xlinear equations that arise
and y-intercepts
when finding x- and
(page 196)
y-intercepts (page 195)
Excel: Linear graphs
SkillSHEET 5.8: Graphing
(page 195)
linear equations using the Cabri geometry: Gradient
x- and y-intercept method
of a straight line
(page 195)
(page 195)
Game time 001 (page 195)
(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)
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
5

Perpendicular lines
(page 198)
WE 6
Ex 5D Perpendicular lines
(page 199)
Investigation: Pairs of
perpendicular lines
(page 198)
Formula for finding the
equation of a straight line
Investigation: Which
phone company is
Excel: Perpendicular
checker (page 199)
GC tip  TI: Viewing
perpendicular lines
(page 199)
Game time 002 (page 202)
WorkSHEET 5.2
Mathcad: Equation of a
straight line (page 202)
describing the equation
of a line as the
relationship between
the x- and ycoordinates of any
point on the line
 sketching the graph of
a line by finding the xand y-intercepts from
its equation
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)
PAS5.3.3
 finding the equation of
6
(page 200)
WE 7, 8
Ex 5E Formula for finding
the equation of a straight
line (page 202)
Graphs of linear
inequalities (page 204)
WE 9, 10, 11, 12
Ex 5F Graphs of linear
inequalities (page 207)
cheaper? (page 203)
10 Quick Questions 2
(page 209)
(page 202)
SkillSHEET 5.9: Checking
whether a given point
makes the inequality a
true statement (page 207)
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)
Mathcad: Horizontal and
vertical graphs
(page 207)
Graphmatica (page 208)
GrafEq (page 208)
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
PAS5.3.3
 graphing inequalities
of the form y < a,
y > a, y  a, y  a,
x < a, x > a, x  a and
xa
on the number plane
 graphing inequalities
such as y  x on the
number plane by
considering the position
of the boundary of the
7
Distance between two
points (page 209)
WE 13
Ex 5G Distance between
two points (page 210)
Midpoint of a segment
(page 212)
WE 14, 15
Ex 5H Midpoint of a
segment (page 213)
Investigation: A Roman
aqueduct (page 262)
SkillSHEET 5.10: Using
Pythagoras’ theorem
(page 210)
Mathcad: Distance
between two points
(page 210)
Excel: Distance between
two points (page 210)
GC program  Casio:
Distance between two
points (page 210)
GC program  TI:
Distance between two
points (page 210)
Cabri geometry: Distance
between two points
(page 210)
WorkSHEET 5.3
(page 213)
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)
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 + y < 7, 2x  3y  5
PAS5.2.3
 using Pythagoras’
theorem to establish the
formula for distance, d,
between two points
( x1 , y1 ) and ( x2 , y 2 ) 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)
PAS5.2.3
 using the average
concept to establish the
formula for the
midpoint, M, of the
interval joining two
points ( x1 , y1 ) and
( x2 , y 2 ) on the number
plane
8
Cabri geometry: Midpoint
of a segment (page 213)
Summary (page 214)
Chapter review (page 215)
 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)
‘Test yourself’ multiple
choice questions
Topic tests (2)
9