The Cartesian Plane

• Understand the Cartesian coordinate system named after René Descartes.
• Identify x-axis, y-axis, and origin (0, 0).
• Name the four quadrants and signs of coordinates in each.
• Plot and read ordered pairs (x, y).
• Relate coordinates to maps, seating plans, and NCERT Ex. 3.1.

1. Axes — Two perpendicular number lines: horizontal x-axis, vertical y-axis.
2. Origin — Intersection point O = (0, 0).
3. Ordered pair — (x, y): x = abscissa (horizontal), y = ordinate (vertical).
4. Quadrants — I (+,+), II (−,+), III (−,−), IV (+,−) — anticlockwise from positive x.
5. Points on axes — On x-axis: y = 0; on y-axis: x = 0.
6. Half-planes — x > 0 (right), x < 0 (left), y > 0 (above), y < 0 (below).
7. Real-world link — Street grids, chess boards, pixel screens use coordinate ideas.
8. NCERT — Plot (−2, 3), (3, −1), (−1, −2); state quadrant of each.
9. Perpendicular distance to axes — |x| to y-axis, |y| to x-axis.
10. One-to-one — Each ordered pair ↔ unique point in plane (for given axes).

NCERT: State quadrant of points A(−3, 2), B(4, −1), C(−2, −5), D(5, 3)

A(−3, 2): x negative, y positive → **Quadrant II**
B(4, −1): x positive, y negative → **Quadrant IV**
C(−2, −5): both negative → **Quadrant III**
D(5, 3): both positive → **Quadrant I**
Points on axes do not lie in any quadrant

• Swapping (x, y) order — (3, 2) ≠ (2, 3) in general.
• Saying (0, 4) is in Quadrant I (points on axes are not in any quadrant).
• Quadrant numbering anticlockwise vs clockwise confusion.
• Confusing abscissa with ordinate.
• Plotting (−2, −3) in Quadrant II instead of III.

• Write coordinates of origin.
• In which quadrant is (−5, −1)?
• What is the y-coordinate of any point on the x-axis?
• Signs of coordinates in Quadrant IV?
• Distance from (7, 0) to y-axis?

Open the Practice tab for graded questions on The Cartesian Plane.