Download Graphmatica (page 390)

1
WORK PROGRAM
Chapter 10 Coordinate geometry
Strands: Patterns and algebra, Measurement
Substrands and outcomes:
Algebraic techniques
PAS4.4 Uses 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
Perimeter and area
MS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and
figures composed of rectangles and triangles
Section
Are you ready? (page 362)
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 362)
10.1: Substitution into a
rule
10.2: Completing a table
of values for a given rule
10.3: Plotting coordinate
points
10.4: Matching a graph
with its table of values
10.5: Plotting a line using
a table of values
Technology applications
(CD-ROM)
Learning outcomes
PAS4.4
 solving equations arising from
substitution into formulae
PAS4.5
 reading and plotting ordered
pairs on the number plane
including those with values
that are not whole numbers
 forming a table of values for a
linear relationship by
substituting a set of
2
10.12: Using Pythagoras’
theorem
Plotting linear graphs
(page 363)
WE 1
Ex 10A Plotting linear
graphs (page 366)
History of mathematics:
René Descartes
(page 363)
appropriate values for either
of the letters and graphing the
number pairs on a number
plane
MS4.1
 using Pythagoras’ theorem to
find the length of sides in
right-angled triangles
SkillSHEET 10.1:
Cabri geometry: Linear
PAS4.5
Substitution into a rule
patterns and equations
 forming a table of values for a
(page 366)
(page 365)
linear relationship by
SkillSHEET 10.2:
Cabri geometry:
substituting a set of
Completing a table of
Coordinates and graphs
appropriate values for either
values for a given rule
(page 366)
of the letters and graphing the
(page 366)
Excel: Plotting graphs
number pairs on a number
SkillSHEET 10.3: Plotting
(tables) (page 366)
plane
coordinate points
Excel: Plotting graphs
PAS5.1.2
(page 366)
(tables) (DIY) (page 366)  constructing tables of values
SkillSHEET 10.4:
Excel: Plotting graphs
and using coordinates to
Matching a graph with its
(rule) (page 366)
graph vertical and horizontal
table of values
Mathcad: Plotting linear
lines
(page 366)
graphs (page 366)
 identifying the x-axis as the
SkillSHEET 10.5: Plotting
line y = 0
a line using a table of
 identifying the y-axis as the
values (page 366)
line x = 0
Game time 001 (page 367)
 graphing a variety of linear
relationships on the number
plane by constructing a table
of values and plotting
coordinates using an
appropriate scale
 describing horizontal and
3
Gradient and y-intercept
(page 367)
WE 2, 3a–b, 4
Ex 10B Gradient and
y-intercept (page 370)
Maths Quest challenge:
Q1–3 (page 374)
10 Quick Questions 1
(page 374)
Investigation: Gradient
and y-intercept
(page 375)
SkillSHEET 10.6:
Measuring the rise and
run (page 371)
SkillSHEET 10.7: Finding
the gradient given to two
points (page 372)
Worksheet 10.1 (page 373)
Cabri geometry: Gradient
(pages 368, 370)
Excel: Gradient and
intercepts (page 370)
Excel: Gradient and
intercepts DIY
(page 370)
Mathcad: Gradient
(page 372)
Excel: Gradient (page 372)
Cabri geometry: Linear
graphs and y-intercept
(page 375)
Cabri geometry: Linear
equations and gradient
(page 375)
vertical lines in general terms
(Communicating)
PAS5.1.2
 using the right-angled triangle
drawn between two points on
the number plane and the
rise
relationship 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
 finding the gradient of a
straight line from the graph by
drawing a right-angled
triangle after joining two
points on the line
 identifying the x- and
y-intercepts of graphs
 graphing a variety of linear
relationships on the number
plane by constructing a table
of values and plotting
coordinates using an
appropriate scale
PAS5.2.3
 using the relationship
rise
gradient =
to establish
run
4
Determining the equation
of a straight line
(page 376)
WE 5, 6, 7
Ex 10C Determining the
Code puzzle (page 379)
Investigation: Relating
equations and graphs to
values of gradients and
intercepts (page 380)
Game time 002 (page 378)
SkillSHEET 10.8: Finding
the gradient of a line
from its equation
(page 381)
Mathcad: Equation of a
straight line (page 378)
Excel: Equation of a
straight line (page 378)
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
 constructing tables of values
and using coordinates to
graph straight lines of the
form y = mx + b
 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 the difference in
equations of lines that have a
negative gradient and those
that have a positive gradient
(Reasoning)
 comparing similarities and
differences between sets of
linear relationships
(Reasoning)
PAS5.2.3
 recognising equations of the
form y = mx + b as
representing straight lines and
interpreting the x-coefficient
5
equation of a straight line
(page 378)
(m) as the gradient and the
constant (b) as the y-intercept
 rearranging an equation in
general form to the
gradient/intercept form
 graphing equations of the
form y = mx + b using the
y-intercept (b) and the
gradient (m)
 determining that two lines are
parallel if their gradients are
equal
 finding the gradient and the yintercept of a straight line
from the graph and using
them to determine the
equation of the line
 determining the difference in
equations of lines that have a
negative gradient and those
that have a positive gradient
(Reasoning)
 matching equations of straight
lines to graphs of straight
lines and justify choices
(Communicating, Reasoning)
PAS5.3.3
 describing the equation of a
line as the relationship
between the x- and ycoordinates of any point on
the line
6

Sketching straight line
graphs (page 382)
WE 8, 9
Ex 10D Sketching straight
line graphs (page 384)
Investigation: Predicting a
person’s height
(page 385)
10 Quick Questions 2
(page 385)
SkillSHEET 10.9: Solving Excel: Linear graphs
linear equations that arise
(page 384)
when finding x- and
Mathcad: Linear graphs
y-intercepts (page 384)
(page 384)
SkillSHEET 10.10:
Mathcad: Linear graphs —
Graphing linear
intercept form (page 384)
equations using the xand y-intercept method
(page 384)
WorkSHEET 10.2
(page 384)
finding the equation of a line
passing through two points
PAS5.1.2
 identifying the x- and yintercepts of graphs
 identifying the x-axis as the
line y = 0
 identifying the y-axis as the
line x = 0
 graphing a variety of linear
relationships on the number
plane by constructing a table
of values and plotting
coordinates using an
appropriate scale
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
 graphing equations of the
form y = mx + b using the yintercept (b) and the gradient
(m)
 finding the gradient and yintercept of a straight line
from the graph and using
them to determine the
equation of the line
7

Graphs of linear
inequalities (page 386)
WE 10, 11, 12, 13
Ex 10E Graphs of linear
inequalities (page 389)
SkillSHEET 10.11:
Checking whether a
given point makes the
inequation a true
statement (page 389)
Mathcad: Horizontal and
vertical graphs
(page 389)
GraphEq (page 390)
Graphmatica (page 390)
applying knowledge and skills
of linear relationships to
practical problems (Applying
strategies)
PAS5.3.3
 sketching the graph of a line
by finding the x- and yintercepts from its equation
PAS5.3.3
 rearranging equations from
the general form to the
gradient/intercept form and
hence graphing the line
 sketching the graph of a line
by finding the x- and
y-intercepts from its equation
 graphing inequalities of the
form y < a, y > a, y  a, y 
a, x < a, x > a, x  a and x 
a
 graphing inequalities such as
y  a on 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
8
Parallel lines (page 391)
WE 14, 15
Ex 10F Parallel lines
(page 393)
Investigation:
Investigating linear
equations (page 391)
Perpendicular lines
(page 394)
WE 16
Ex 10G Perpendicular
lines (page 395)
Investigation: Pairs of
perpendicular lines
(page 394)
Maths Quest Challenge:
Q1–2 (page 396)
WorkSHEET 10.3
(page 405)
GC tip — Casio: (page
391)
Excel: Plotting points
(page 392)
Excel: Gradient (page 393)
Mathcad: Gradient
(page 393)
Cabri geometry: Gradient
(page 393)
Excel: Parallel checker
(page 393)
GC program — Casio:
Parallel checker
(page 393)
GC program — TI:
Parallel checker (page
393)
Excel: Perpendicular
checker (page 395)
x  y  7, 2 x  3 y  5
PAS5.1.2
 determining whether a point
lies on a line by substituting
into the equation of the line
PAS5.2.3
 rearranging an equation in
general form to the
gradient/intercept form
 determining that two lines are
parallel if their gradients are
equal
 using a graphics calculator to
graph a variety of equations
of straight lines, and compare
and describe the similarities
and differences between the
lines (Applying strategies,
Communicating, Reasoning)
PAS5.3.3
 rearranging equations in the
gradient/intercept form to the
general form
 describe conditions for lines
to be parallel (Reasoning,
Communicating)
PAS5.2.3
 rearranging an equation in
general form to the
gradient/intercept form
PAS5.3.3
9

Distance between two
points (page 397)
WE 17, 18, 19
Ex 10H Distance between
two points (page 399)
SkillSHEET 10.12: Using
Pythagoras’ theorem
(page 399)
Mathcad: Distance
between 2 points
(page 399)
Excel: Distance between 2
points (page 399)
GC program — Casio:
Distance between 2
points (page 399)
GC program — TI:
Distance between 2
points (page 399)
demonstrating that two lines
are perpendicular if the
product of their gradients is
–1
 showing that if two lines are
perpendicular then the
product of their gradients is
–1 (Applying strategies,
Reasoning, Communicating)
 proving that a particular
triangle drawn on the number
plane is right-angled
(Applying strategies,
Reasoning)
PAS5.1.2
 graphing two points to form
an interval on the number
plane and forming a rightangled triangle by drawing a
vertical side from the higher
point and a horizontal side
from the lower point
 using the right-angled triangle
drawn between two points on
the number plane and
Pythagoras’ theorem to
determine the length of the
interval joining the two points
 describing how the length of
an interval joining two points
can be calculated using
Pythagoras’ theorem
10
Midpoint of a line segment
(page 400)
WE 20, 21, 22
Ex 10I Midpoint of a line
segment (page 402)
Mathcad: Midpoint of a
segment (page 402)
Excel: Midpoint of a
segment (page 402)
GC program — Casio:
Midpoint of a segment
(page 402)
GC program — TI:
Midpoint of a segment
(page 402)
Cabri geometry: Midpoint
of a segment (page 402)
(Communicating, Reasoning)
PAS5.2.3
 using Pythagoras’ theorem to
establish the formula for the
distance, d, between two
points (x1, y1) and (x2, y2) on
the number plane
 using the formula to find the
distance between two points
on the number plane
 using the gradient and
distance formulae to
determine the type of triangle
three points will form or the
type of quadrilateral four
points will form and justify
the answer (Applying
strategies, Reasoning)
PAS5.1.2
 determining the midpoint of
an interval from a diagram
 describe the meaning of the
midpoint of an interval and
how it can be found
(Communicating)
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, y2) on the number plane
 using the formula to find the
11
Further equations of a
straight line (page 403)
WE 23, 24, 25, 26a–c
Ex 10J Further equations
of a straight line
(page 407)
Investigation: A Roman
aqueduct (page 408)
WorkSHEET 10.3
(page 408)
Excel: Equation of a
straight line (page 406)
Mathcad: Equation of a
straight line (page 406)
Mathcad: Equation of a
straight line (page 407)
Excel: Equation of a
straight line (page 407)
midpoint of the interval
joining two points on the
number plane
 using the formula to find the
distance between two points
on the number plane
 explaining the meaning of the
pronumerals in the formulae
for midpoint, distance and
gradient (Communicating)
 using the appropriate
formulae to solve problems on
the number plane (Applying
strategies)
PAS5.1.2
 graphing a variety of linear
relationships on the number
plane by constructing a table
of values and plotting
coordinates using an
appropriate scale
PAS5.2.3
 using the formula to find the
gradient of an interval joining
two points on the number
plane
 finding the gradient and
y-intercept of a straight line
from the graph and using
them to determine the
equation of the line
 using the appropriate
12
formulae to solve problems on
the number plane (Applying
strategies)
 applying the knowledge and
skills of linear relationships to
practical problems (Applying
strategies)
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) and
y = mx + b
 finding the equation of a line
passing through two points
 finding the equation of a line
that is parallel or
perpendicular to a given line
Summary (page 409)
Chapter review (page 410)
‘Test yourself’ multiple
choice questions
(page 412)
Topic tests (2)