Download IB Studies Topic 5 prior

Material Taken From:
Mathematics
for the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark
Bruce
Haese and Haese Publications, 2004
AND
Mathematical Studies Standard Level
Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman
Oxford University Press, 2012
vertical y-axis
Cartesian Coordinate Plane
origin
horizontal x-axis
y - axis
Thepoint
first on
number
is thewill
x-coordinate
and with
Every
the graph
be represented
tells
how far
to goinleft
or right.
two you
numbers
written
parenthesis.
x - axis
(4, -3)
The second number is the y-coordinate and
tells you how far to go up or down.
( -, +)
II
y - axis
The axes divide the graph into 4 quadrants.
Each quadrant has a number.
( +, +)
I
x - axis
III
( -, -)
IV
( +, -)
Plot: (-3, 5)
(-4, -2) (4, 3) (3, -4)
Rules of Pythagoras
leg 2
All Triangles:
•The sum of the three angles
equals 180°.
leg 1
Right Triangles:
• One of its angles must be a right
angle (90°).
•The side opposite of the right
angle is called the hypotenuse.
•The other sides of the triangle are
called the legs.
Pythagorean Theorem
a 2 + b 2 = c2
c
a
b
Only works in right triangles
Practice
Find x:
Distance
10
Consider points:
A (2, 2)
B (8, 8)
8
6
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
What is the distance
of the line AB?
Distance Formula
The distance between points A(x1, y1) and B(x2, y2)
is defined as:
d=
AB 
 y2  y1    x2  x1 
2
2
Practice
Find the distance between the following points:
a) (2, -4) and (-5, -1)
b) (0, 3) and (-6, 2)
c) (-9, 12) and (7, 8)
Midpoint
10
Consider points:
A (0, 2)
B (8, 2)
8
6
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
What is the midpoint
of the line AB?
Midpoint Formula
The midpoint M of the line segment joining
A (x1, y1) and B (x2, y2) is:
 x1  x2 y1  y2 
,


2 
 2
Practice
Find the midpoint between the following points:
a) (6, -2) and (2, -9)
b) (-8, -4) and (5, -3)
c) (9, 12) and (-1, 3)
In each of the figures find the:
a) perimeter
b) area
Practice
7 mm
6m
16 mm