082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

4.2 Cartesian coordinate system -- two dimensions 155
y
3
2
1
x coordinate
P
y coordinate
–4 –3 –2 –1 O 1 2 3 4
–1
x
–2
–3
Figure4.1
Cartesian coordinate system in
two dimensions.
When stating the coordinates of a point, by convention we always state thexcoordinate
first. Thus (3, 1) means that thexcoordinate is 3 and theycoordinate is 1. We
also write, for example, A(3, 1) to mean that the point whose coordinates are (3, 1) is
labelled A.InFigure 4.1 Phas coordinates (2, 3).
Example4.1 Plot the points whoseCartesiancoordinates are
(a) (4,2) (b) (−1,−3) (c) (−2,1)
Solution AsplottedinFigure 4.2
(a) Rhas coordinates (4,2).
(b) S has coordinates (−1,−3).
(c) Thas coordinates (−2,1).
Example4.2 Statethe coordinates ofthe points Aand B asshown inFigure 4.3.
Solution Ahas coordinates (−3,−1); Bhas coordinates (3,−2).
y
2
R
y
2
T
1
1
–4 –3 –2 –1 O 1 2 3 4
–1
–2
S
–3
x
–3 –2 –1 O 1 2 3
A
–1
–2
B
–3
x
Figure4.2
Figure4.3