Coordinate Geometry

Coordinate Geometry Prepared by: Low Hui Ming (15)

Location of Singapore y 3 2 (2, 2) 1 0 x 1 2 3 4

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

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.

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

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

x coordinate = y coordinate = Midpoint, M = Finding Midpoint y (1, 3) 3 2 (2, 2) (3, 1) 1 0 x 1 2 3 4

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

Coordinate Geometry