Coordinate Form 2

1. LEVEL : FORM 2
LEARNING AREA:
COORDINATES

2. LEARNING OBJECTIVES:
Understand and use the
concept of distance
between two points on a
Cartesian plane

3. LEARNING OUTCOMES:
(i) Find the distance between two
points with:
(a) common y-coordinates
(b) common x-coordinates
(ii) Find the distance between two
points using Pythagoras’ theorem

4.  HOW FAR IS YOUR SCHOOL FROM HOME ????
 HOW DO YOU MEASURE THE DISTANCE ????

5. DO YOU KNOW WHAT IS
DISTANCE ?
LENGTHS
BETWEEN
TWO POINTS

6. B( 2, 6)
AB = 6 -1
= 5 units
6
4
2
If x-coordinates are the
same, the distance is
the difference between
their y coordinates
1
2
3
4
5
A( 2, 1)
2
4
Difference between the x
coordinates ( the larger
value minus the smaller
value)

7. 1
2
3
4
5
6
7
D( 1, 2)
C( -6, 2)
-6
-4
-2
CD = 1 – (- 6)
= 7 units
2
If y-coordinates are
the same, the
distance is the
difference between
their x coordinates
Difference between the y
coordinates ( the larger value
minus the smaller value)

8. Find the distance between point P(2,1) and point Q(8,9)
1. Draw a right
angle triangle
joining point P
and point Q.
Q( 8, 9)
1
2
3
2. Label the point
of intersection
of the two line
as R
3. Count/
calculate the
number of
units for
length PR and
QR
4
5
6
7
P( 2, 1)
8
R
1
2
3
4
5
6

9. 4. By using
Pythagaros’
theorem,
calculate the
length of PQ.
PQ =
2
+
2
Q( 8, 9)
=
10
8
P( 2, 1)
R
6

10. By using Pythagaros’
theorem, calculate the
length of PQ.
AB = 6 + 8
= 10
2
A ( 6, 9 )
2
B( -2,3 )
9-3=6
6-(-2)=8

11. By using Pythagaros’ theorem, find the distance
between point A( 9 , 4) and point B( 5 , 2 ).
AB = ( − ) + ( − )
2
= 4 +3
2
=5
2
2

12. By using Pythagaros’ theorem, find the distance
between point P( -1, -4 ) and point Q( -6 , 8 ).
AB = (−1 − (−6) + (−4 − 8)
2
= 5 + (−12)
2
= 25 + 144
= 13
2
2

13. TOPIC
: COORDINATES
SUBTOPIC : MIDPOINTS

14. LEARNING OUTCOMES:
i. Identify the midpoint of a straight line
joining two points.
ii. Find the coordinates of the midpoints of
a straight line joining two points with:
a. common y - coordinates.
b. common x - coordinates.
iii. Find the coordinates of the midpoints of
the line joining two points.
iv. Pose and solve problems involving
midpoints.

15. UNDERSTAND & USE THE
CONCEPT OF MIDPOINTS
IDENTIFY THE
MIDPOINTS

16. *The tree is located in the middle of the
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
5 km
KM
5 km

17. MIDPOINT
MIDPOINT
10
5 km
KM
5 km
The midpoint is the point that divides a line
into two equal parts

18. LETS IDENTIFY THE MIDPOINTS
0 unit
2 units
4 units
6 units
The midpoint between drummer and Mr B
8 units
10 units
mice
The midpoint between drummer and Dancing man
Mr B
The midpoint between the mice and the tree
House

19. The midpoint of
AB = (3 , 4 )
B( 3, 8 )
8
4
6
When the x-coordinates
of the two points are
the same, then the xcoordinate of the
midpoint remains the
same.
The y –coordinate of the
midpoint = 8+0 = 4
2
4M ( 3 , 4 )
4
2
2
4
A( 3, 0)

20. P( -2, 3 )
The midpoint
of PQ = (-2,-2 )
2
5
M ( -2 , -2 )
-2
2
-2
When the x-coordinates
of the two points are
the same, then the xcoordinate of the
midpoint remains the
same.
5
-4
-6
Q( -2, -7)
The y –coordinate of the
midpoint = 3+(-7) = -2
2

21. P( 2, 6)
Q( 8, 6)
3
2
3
4
6
X –coordinate of the
midpoints = 2 + 8 = 5
2
The midpoint of PQ =
= ( 5, 6 )
8
When the ycoordinates of the
two ponits are the
same, the ycoordinate of the
midpoint remains
the same

22. The midpoint of PQ =
= ( -1, 2 )
B( 2, 2)
A( -4, 2)
3
-4
3
-2
2
X –coordinate of the
midpoints = -4 + 2 = -1
2
4
When the y-coordinates
of the two ponits are the
same, the y- coordinate
of the midpoint remains
the same

23. COORDINATES OF THE
MIDPOINT OF A LINE JOINING
y
TWO POINTS
Q( 11, 8 )
Q ( x2 , y2 )
M(6, 5)
8+2=5
5
2
y1 +y 2
2
P( 1, 2 )
P ( x1 , y1 )
0
x
6
1 + 11 = 6
2
x1 + x2
2

24. MIDPOINT OF A LINE
JOINING TWO
POINTS
MIDPOINT
( x, y )
=
 x1 + x2 y1 + y2 
,

÷
2 
 2

25. Y
Find the midpoint of PQ?
Q( 8, 7)
Midpoint PQ=
M
 2 +8 1 + 7 
,

÷
2 
 2
P( 2, 1)
0
 X 1 + X 2 Y1 + Y2 
,

÷
2
2 

X
10 8 

,

÷
2
2

5, 4 )
((5, 4 )

26. y
Based on
the diagram:
1.State the
midpoint of
AB.
2.C is the
midpoint of
AD, state
the
coordinates
of D.
3.Q is the
midpoint of
PR, state the
coordinates
of P.
Answers:
4
C
1. (3, 2)
B
2. D(1, 5)
3. (-2, 1)
2
A
-4
-2
2
-2
-4
Q
4
6
R( 5,-3)
8
x

27. Based on
the
diagram
:
1.State the
midpoint of
AB
CB
2.If ABCD
forms
a
rectangl
e,
-4
write the
coordinates
of D.
3.Q is the
midpoint of
PR, state
the
coordinates
of P.
y
Answers:
C
1. a. (4,1)
b. (4,3)
4
2
A
2. D(7,5)
B
3. P(-1,-1)
-2
2
4
6
8
-2
Q
-4
R( 5,-3)
x

28. In the diagram, B is the midpoint of the straight line AC.
What is the value of k?
y
A( -2,12)
Answers:
k = -2
B( 2,5)
x
0
C( 6,k)

29. The diagram shows
a right-angled triangle
ABC.
y
The sides AB
and AC are parallel
to the y-axis and
x-axis respectively.
The length of AB
is 6 units.
If M is the midpoint of
BC,
Find the value of p.
B
M( 2,p )
A( 1, 1)
0
C( 3,1)
x
Answers:
p=4

30. CREATED BY:
CHEONG SHU LIN
CHYE SOO FUEN
WAN ZAKIAH WAN MUSTAPHA
ZAIMIRA JAILANI
ZARINA MAAROF