Point Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Point.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

An exact location in space with no size, length, or width—zero dimensions; named with a capital letter.

The tip of a pencil or a dot on a map. Position only, no width or length.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Points are the most basic geometric objects—they have position but no extent.

Common stuck point: A drawn dot has size, but the mathematical point it represents doesn't.

Sense of Study hint: Ask yourself: does this location need any length or width to describe it? If no, you are thinking of a point.

Worked Examples

Example 1

easy
Plot the point (3, 2) on a coordinate grid and describe its location.

Solution

  1. 1
    Step 1: Start at the origin (0, 0).
  2. 2
    Step 2: Move 3 units to the right along the x-axis.
  3. 3
    Step 3: Move 2 units up along the y-axis.
  4. 4
    Step 4: Mark that location with a dot — this is the point (3, 2).

Answer

The point (3, 2) is 3 units right and 2 units up from the origin.
A point has no size, no length, no area — it is simply a location in space. On a 2D coordinate grid, every point is uniquely identified by an ordered pair (x, y).

Example 2

medium
Points A(1,1), B(4,1), and C(4,5) are three corners of a rectangle. What are the coordinates of the fourth corner D?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What are the coordinates of the origin on a standard coordinate grid?

Example 2

hard
In 3D space, describe the point (2, -3, 5). How does adding a third coordinate change what a point represents compared to 2D?
← Back to Point Practice Mode

Related Concepts

LineCoordinate Plane