Coordinate Geometry

1. Coordinate Geometry

2. Location of Singapore

y
3
2
(2, 2)
1
0
1
2
3
4
x

3. Objectives

describe Cartesian coordinates in two
dimensions (x, y)
finding the distance and midpoint when
given two Cartesian coordinates

4. History

Developed by a sick mathematician, Rene'
Descarte.
As he lay in bed sick, he saw a fly buzzing
around on the ceiling. His ceiling was made of
square tiles. As he watched, he realized that
he could describe the position of the fly by
the ceiling tile he was on.

5. Uses

Cinema tickets
Street directory
Latitudes and longtitudes
Maps in shopping centres
Labels of HDB blocks

6. Distance

= (x2 x1)2 + (y2 y1)2
y
3
Recall: Pythagoras’ Theorem
Hypothenus2 = Length2 + Breadth2
(2, 2)
2
difference in y
2 units
1
0
1
difference in x
3 units
2
3
(5, 0)
4
5
x

7. Finding Midpoint

y
(1, 3)
3
3 1
2
x coordinate =
2
1 3
y coordinate =
2
2
2
(2, 2)
(3, 1)
1
x1 x2 y1 y2
,
Midpoint, M =
2
2
0
1
2
3
4
x

8. Conclusion

able to identify Cartesian coordinates in
two dimensions
calculate the distance and midpoint when
given two Cartesian coordinates