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Coordinate Geometry Practice

Solve chapter-level practice questions for Coordinate Geometry with reveal-only solutions and quick revision support.

Practice Set 1 — Cartesian Plane and Quadrants

Naming quadrants, signs of coordinates, points on axes.

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Q1.
Write the quadrant or axis for each point: (3, 5), (−2, 4), (−7, −1), (6, −3), (0, 5), (−4, 0).
Q2.
What are the coordinates of the origin?
Q3.
In which quadrant or on which axis does a point lie if its abscissa is 0 and ordinate is −6?
Q4.
If the x-coordinate of a point is positive and its y-coordinate is negative, where does the point lie?
Q5.
Name the point where the two axes cross and give the sign pattern of each quadrant.
Q6.
State whether true or false: the point (0, 0) lies in the first quadrant.

Practice Set 2 — Plotting and Reasoning

Plotting points, lines of constant x or y, simple figures.

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Q1.
Describe how to plot the point (−3, 2).
Q2.
Points (1, 3), (1, −2) and (1, 5) are plotted. What can you say about them?
Q3.
The points A(2, 3), B(2, −1), C(−2, −1) and D(−2, 3) are plotted and joined in order. What figure is formed?
Q4.
Where do all points of the form (x, 0) lie?
Q5.
A point has ordinate −4 and lies on the line x = 3. Write its coordinates and quadrant.
Q6.
Plot the points (0, 0), (4, 0), (4, 3) and find the length of the horizontal and vertical sides of the triangle formed with the origin.

Quick Q&A Before You Revise

Why is (x, y) called an ordered pair?

Because the order of the numbers matters: the first number is always the x-coordinate and the second is always the y-coordinate. (2, 5) and (5, 2) represent different points.

Do points on the axes belong to a quadrant?

No. Points on the x-axis or y-axis (including the origin) lie on the boundary and are not counted in any of the four quadrants.

How do you know the quadrant of a point without plotting it?

Look only at the signs of its coordinates: (+, +) is I, (−, +) is II, (−, −) is III, (+, −) is IV.

What is the perpendicular distance of the point (5, −3) from the x-axis and from the y-axis?

Distance from the x-axis is |y| = 3 units; distance from the y-axis is |x| = 5 units.

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