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Example 2: In which quadrant will the following points lie?

(a) P(5, 6) (b) Q(9, –8) (c) R(–3, 11) (d) S(–1, –9)

Solution: (a) In point P(5, 6), both coordinates are positive.

\ Point P(5, 6) will lie in Quadrant I.
(b) In point Q(9, –8), the x-coordinate is positive and the y-coordinate is negative.

\ Point Q(9, –8) will lie in Quadrant IV.

(c) In point R(–3, 11), the x-coordinate is negative and the y-coordinate is positive.

\ Point R(–3, 11) will lie in Quadrant II.

(d) In point S(–1, –9), both coordinates are negative.
\ Point S(–1, –9) will lie in Quadrant III.

Locating a Point on a Cartesian Plane

To locate the coordinates of a point, follow these steps:

Step 1: Draw perpendiculars from the given point on the x-axis and y-axis.

Step 2: Count the number of units along x-axis and y-axis as the distance from zero to the point
where the perpendicular meets x-axis and y-axis respectively.

Step 3: Write the coordinates obtained as an ordered pair (a, b), where ‘a’ represents the x-coordinate
and ‘b’ represents the y-coordinate of the point.

Example 3: Locate the coordinates of the points A, B, C, and D from the given Cartesian plane.

Y
5

4

B
3
A
2

1

X –5 –4 –3 –2 –1 O 1 2 3 4 5 X
–1
–2

–3

–4
C
–5
D Y

317 Introduction to Graphs