NCERT Solutions for Class 9th Maths Chapter 1 In-text Questions — The 2-d Cartesian Coordinate System
Book page 6 Updated on2026-09-08
Q1.
So far, we have only considered points on the two coordinate axes. What can you say about the coordinates of points that are not on either axes?
Answer
Both coordinates are non-zero, and their two signs together decide which of the four quadrants the point is in.
The four quadrants. The sign pair (x-sign, y-sign) is the address of a quadrant.
Quadrant
Position
Sign of x
Sign of y
I
right of the y-axis, above the x-axis
+
+
II
left of the y-axis, above the x-axis
−
+
III
left of the y-axis, below the x-axis
−
−
IV
right of the y-axis, below the x-axis
+
−
Why it happens: To reach a point from O you make two independent moves: a horizontal shift and a vertical shift. Each shift has a size and a direction, and the sign convention records the direction — right and up are positive, left and down are negative. Since each of the two signs can be chosen in 2 ways, there are 2 × 2 = 4 possible sign patterns, and that is precisely why the axes cut the plane into four quadrants, no more and no fewer.
Why the axes belong to no quadrant: A point on an axis is the case where one of the two shifts is zero, and zero is neither positive nor negative. (x, 0) sits on the x-axis, (0, y) sits on the y-axis, and O (0, 0) has both shifts zero. These are the boundary cases between quadrants, which is why they are counted separately.
Tip: To name the quadrant of a point you never need to plot it. Just read the two signs. (−7, 2) is (−, +), so Quadrant II. (0.5, −9) is (+, −), so Quadrant IV.