Page 18 - Calculus Demystified

5
Basics
CHAPTER 1
1.3 Coordinates in Two Dimensions
We locate points in the plane by using two coordinate lines (instead of the single
line that we used in one dimension). Refer to Fig. 1.6. We determine the coordinates
of the given point P by first determining the x-displacement, or (signed) distance
from the y-axis and then determining the y-displacement, or (signed) distance from
the x-axis. We refer to this coordinate system as (x, y)-coordinates or Cartesian
coordinates. The idea is best understood by way of some examples.

y

P

x

Fig. 1.6

EXAMPLE 1.4
Plot the points P = (3, −2), Q = (−4, 6), R = (2, 5), S = (−5, −3).

SOLUTION
The first coordinate 3 of the point P tells us that the point is located 3 units
to the right of the y-axis (because 3 is positive). The second coordinate −2of
the point P tells us that the point is located 2 units below the x-axis (because
−2 is negative). See Fig. 1.7.
The first coordinate −4 of the point Q tells us that the point is located 4 units
to the left of the y-axis (because −4is negative). The second coordinate 6 of
the point Q tells us that the point is located 6 units above the x-axis (because
6 is positive). See Fig. 1.7.
The first coordinate 2 of the point R tells us that the point is located 2 units
to the right of the y-axis (because 2 is positive). The second coordinate 5 of the
point R tells us that the point is located 5 units above the x-axis (because 5 is
positive). See Fig. 1.7.
The first coordinate −5 of the point S tells us that the point is located 5 units
to the left of the y-axis (because −5is negative). The second coordinate −3of
the point S tells us that the point is located 3 units below the x-axis (because
−3 is negative). See Fig. 1.7.