3. Before draw the scale we should know about four
quadrant.
This is quadrant I, quadrant II, quadrant III and
quadrant I V.
Quadrant I refer to positive (+) where the x-axis
and y-axis is positive.
Quadrant II refer to negative and positive where
the x-axis is negative and y-axis is positive.
Quadrant III refer to negative(-) where the x-axis
and y-axis is negative.
Quadrant IV refer to positive and negative where
the x-axis is positive and y-axis is negative.
4. Do you know more to understand?
Look here!!
y
QUADRANT II
QUADRANT I
2
1
-2
-1
0
1
2
3
-1
QUADRANT III
-2
QUADRANT IV
x
5. Every scale has desided in question
Example:
Mark the values on the x-axis and the y-axis on a
Cartesian plane if the scale for the x-axis
is 1 : 2
and the scale for the y-axis is 1 : 5.
1 unit(1 cm in
graph paper) on the x-axis
represents 2 units
1 unit (1 cm in graph paper) on the y-axis
represents 5 units .
7. How to student plot the point?
Start read the point by x-axis
For example:
A(4,-1) =4 for x-axis and -1 for y-axis
y
2
1
-1
0
1
-1
-2
2
3
4
x
A(4,-1)
8. The distance between two points is the length of the
straight line which joins the two points.
Find the distance two point?
i.
Points with common y-coordinates .
The straight line which joins two points that have the
same y-coordinates is parallel to the x-axis. Therefore,
the distance between two points, with common ycoordinates is the difference between their xcoordinates.
ii. Points with common x-coordinates
The straight line which joins two points that have the
same x-coordinates is parallel to the y-axis. Therefore,
the distance between two points with common xcoordinates is the difference between their ycoordinates.
9. A and B refer to common x-coordinates
C and D refer to common y-coordinates
y
x-coordinates
-2
A
2
1
-1
B
0 C
-1
1
2
3
D
-2
y-coordinates
x
10. How to calculate the distance?
Common x-coordinates
Distance between A and B
=2-(2)
=2+2
=4 units
Common y-coordinates
Distance between C and D
=2-(-1)
=2+1
=3 units
Please read at y-axis
to calculate common
x-coordinate
Please read at y-axis
to calculate common
x-coordinate
11. The
distance between any two points with
different x-coordinates and y-coordinates is the
length of the straight line joining the two points.
The straight line is the hypotenuse of a rightangled triangle where its two other sides
are parallel to the x-axis and y-axis respectively.
a
Formula=
ab2= √(a-c)2+(c-b)2
c
b
12. Formula=
Ab2= √((a-c)2+(c-b)2 )
ab2 = √((6-2)2+(6-1)2 )
= √(4)2 +(5)2
= √ 41
=6.4 units
Example
Y
a
Hypotenuse
6
4 units
4
2
0
c
b
5 units
2
4
6
X
13. Identify the midpoints of straight lines
The midpoint of a line joining two points is the point that
divides the line into two equal parts
a
||
x
||
b
midpoint
14. Y
Common y-coordinate
Midpoint of AB(0,3)
A(-2,3) ||
3
||
B(2,3)
C(3,2)
2
1
-2
-1
0
-1
-2
X
1
2
3
4
Common x-coordinate
Midpoint of CD(3,0)
D(3,-2)
15. Example
Common y-coordination
Find the coordination of the midpoint of a line joining
point A(-2,3) and B(2,3).
Solution
X-coordinate for the midpoint = (-2+2)/2
= 0/2
=0
Y-coordinate for the midpoint=3
Therefore, the midpoint for the line AB
is(0,3)
16. Example
Common x-coordinate
Find the coordination of the midpoint of a line joining
point C(3,2) and D(3,-2).
Solution
y-coordinate for the midpoint = (2+(-2))/2
= 0/2
=0
x-coordinate for the midpoint=3
Therefore, the midpoint for the line AB
is(3,0)
17. Midpoint = sum of x-coordinates , sum of y-coordinates
2
2
Can use this formula when
coordinate at x-coordinate and
y-coordinate is not same
18. Example
Find the coordinates of the midpoint of the line
joining S(3,1) T1,-5).
Solution
X-coordinate of the midpoint
= 3+1/2
=4/2
=2
Y-coordinate of the midpoint
=1-(-5)/2
=6/2
=3
Therefore, the coordinates of the midpoint of line ST
are(2,3)
