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LEVEL : FORM 2LEVEL : FORM 2
LEARNING AREA:LEARNING AREA:
COORDINATESCOORDINATES
LEARNING OBJECTIVES:LEARNING OBJECTIVES:
Understand and use Understand and use the concept of distance the concept of distance between two points on between two points on
a Cartesian planea Cartesian plane
LEARNING OUTCOMES:LEARNING OUTCOMES:
(i) Find the distance between two (i) Find the distance between two points with:points with:
(a) common y-coordinates(a) common y-coordinates
(b) common x-coordinates(b) common x-coordinates
(ii) Find the distance between two (ii) Find the distance between two points using Pythagoras’ theorempoints using Pythagoras’ theorem
HOW FAR IS YOUR SCHOOL FROM HOW FAR IS YOUR SCHOOL FROM HOME ????HOME ????
HOW DO YOU MEASURE THE HOW DO YOU MEASURE THE DISTANCE ????DISTANCE ????
DO YOU KNOW WHAT ISDO YOU KNOW WHAT IS
DISTANCE ?DISTANCE ?
LENGTHS BETWEEN
TWO POINTS
AB = 6 -1
= 5 units
1
2
3
4
A( 2, 1)
B( 2, 6)
5If x-coordinates are the same, the distance is
the difference between their y coordinates
Difference between the x coordinates ( the larger value minus the smaller
value)
2
6
4
4
2
CD = 1 – (- 6)
= 7 units
1 2 3 4
D( 1, 2)C( -6, 2)
5 6 7
Difference between the y coordinates ( the larger value
minus the smaller value)
If y-coordinates are the same, the distance is the
difference between their x coordinates
-2-4-6 2
1 2 3 4
P( 2, 1)
Q( 8, 9)
52 6
8
7
6
5
4
3
2
1
1. Draw a right angle triangle joining point P and point Q.
R
2. Label the point of intersection of the two line as R
3. Count/ calculate the number of units for length PR and QR
Find the distance between point P(2,1) and point Q(8,9)
P( 2, 1)
Q( 8, 9)
4. By using Pythagaros’ theorem, calculate the length of PQ.
R
22PQ
10
6
8
B( -2,3 )
A ( 6, 9 )
10
86 22
AB
By using Pythagaros’ theorem, calculate the length of PQ.
9-3=6
6-(-2)=8
By using Pythagaros’ theorem, find the distance between point A( , ) and point B( , ).
22 34
5
9 54 2
22 )()( AB
By using Pythagaros’ theorem, find the distance between point P( -1, -4 ) and point Q( -6 , 8 ).
22 )84()6(1( AB
22 )12(5
14425
13
TOPIC : TOPIC : COORDINATESCOORDINATES
SUBTOPIC : MIDPOINTSSUBTOPIC : MIDPOINTS
LEARNING OUTCOMESLEARNING OUTCOMES::i.i. Identify the midpoint of a straight line Identify the midpoint of a straight line
joining two points.joining two points.ii.ii. Find the coordinates of the midpoints Find the coordinates of the midpoints
of a straight line joining two points of a straight line joining two points with:with:a. common a. common yy- coordinates.- coordinates.b. common b. common xx- coordinates.- coordinates.
iii.iii. Find the coordinates of the midpoints Find the coordinates of the midpoints of the line joining two points.of the line joining two points.
iv.iv. Pose and solve problems involving Pose and solve problems involving midpoints.midpoints.
UNDERSTAND & USE THE UNDERSTAND & USE THE CONCEPT OF MIDPOINTSCONCEPT OF MIDPOINTS
IDENTIFY THEIDENTIFY THE
MIDPOINTSMIDPOINTS
10 KM
5 km 5 km
*The tree is located in the *The tree is located in the middlemiddle of the of the drummer and the house. drummer and the house.
*What is the distance between the drummer and the tree?
*What is the distance between the house and the tree?
10 KM
5 km 5 km
MIDPOINTMIDPOINT
The midpoint is the point that divides a line into two equal parts
LETS IDENTIFY THE MIDPOINTSLETS IDENTIFY THE MIDPOINTS
0 unit 2 units 4 units 6 units 8 units 10 units
The midpoint between drummer and Mr B
The midpoint between drummer and Dancing man
mice
Mr B
The midpoint between the mice and the tree House
The midpoint of AB = (3 , 4 )
4
A( 3, 0)
B( 3, 8 )
4
When the x-coordinates of the two points are the same, then the x-
coordinate of the midpoint remains the
same.
The y –coordinate of the midpoint = 8+0 = 4
2
2
6
4
4
2
8
M ( 3 , 4 )
The midpoint of PQ = (-2,-2 )
5
Q( -2, -7)
P( -2, 3 )
5When the x-coordinates
of the two points are the same, then the x-
coordinate of the midpoint remains the
same.
The y –coordinate of the midpoint = 3+(-7) = -2
2
2
2
-4
-2
- 2
M ( -2 , -2 )
-6
The midpoint of PQ = = ( 5, 6 )
3
Q( 8, 6)P( 2, 6)
3
X –coordinate of the midpoints = 2 + 8 = 5
2
When the y-coordinates of the two ponits are the
same, the y- coordinate of the midpoint remains
the same
42 6 8
The midpoint of PQ = = ( -1, 2 )
3
B( 2, 2)A( -4, 2)
3
X –coordinate of the midpoints = -4 + 2 = -1
2
When the y-coordinates of the two ponits are the same, the y- coordinate of the midpoint remains
the same
-2 2 4 -4
y
x0
COORDINATES OF THE COORDINATES OF THE MIDPOINT OF A LINE JOINING MIDPOINT OF A LINE JOINING
TWO POINTSTWO POINTS
1 1,P x y
2 2,Q x yQ( 11, 8 )
P( 1, 2 )
8 + 2 = 5
2
1 + 11 = 6
2
5
6
M(6, 5)
221 yy
221 xx
1 2 1 2,2 2
x x y y
MIDPOINT OF A LINE JOINING TWO POINTSMIDPOINT OF A LINE JOINING TWO POINTS
MIDPOINT = ,x y
P( 2, 1)
Q( 8, 7)
M
Find the midpoint of PQ?Find the midpoint of PQ?
Midpoint PQ=
10 8,
2 2
2 8 1 7,
2 2
5,4
Y
X0
1 2 1 2,2 2
X X Y Y
5,4
Based onthe diagram:1.State the midpoint of AB.
2
4
A
R( 5,-3)
2 6
4
-2
-4
-2-4
C B
y
x8
Q
Answers:
2.C is themidpoint of AD, statethecoordinates of D.
3.Q is the midpoint ofPR, state the coordinates of P.
1. (3, 2)
2. D(1, 5)
3. (-2, 1)
2
4
A
R( 5,-3)
2 6
4
-2
-4
-2-4
C
B
y
x8
Q
Answers:
Based onthe
diagram:
1.State the midpoint of ABCB2.If ABCD formsa
rectangle,
write the coordinates of D.3.Q is themidpoint of PR, state
thecoordinates of P.
1. a. (4,1) b. (4,3)
2. D(7,5)
3. P(-1,-1)
In the diagram, B is the midpoint of the straight line AC.What is the value of k?
Answers:k = -2
y
C( 6,k)
x
B( 2,5)
A( -2,12)
0
The diagram showsa right-angled triangleABC.
The sides ABand AC are parallelto the y-axis and x-axis respectively.
The length of ABis 6 units.
If M is the midpoint of BC,
Find the value of p.
B
y
x
C( 3,1)A( 1, 1)
M( 2,p )
0
Answers:p = 4
CREATED BYCREATED BY::
CHEONG SHU LINCHEONG SHU LIN
CHYE SOO FUENCHYE SOO FUEN
WAN ZAKIAH WAN MUSTAPHAWAN ZAKIAH WAN MUSTAPHA
ZAIMIRA JAILANIZAIMIRA JAILANI
ZARINA MAAROFZARINA MAAROF
