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medium difficulty5 min

Lattice point reasoning

A lattice point is a point whose coordinates are both integers.

In one line: Grid intersection means both numbers are whole.

Practice This Concept

Understand it

Lattice points are the clean grid points on graph paper, where both x and y are whole numbers or integers. They are useful for plotting shapes, reading coordinates, and checking whether a point sits exactly on the grid intersections. Fractional or decimal coordinates do not make a lattice point.

Example

(4, -1) is a lattice point, but (2, 3.5) is not.

Formula and rule

A lattice point has integer coordinates of the form (x, y), where x and y are both integers.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1(4, -1) and (-3, 2) are lattice points because both coordinates are integers.
  2. 2But (1, 2.5) is not a lattice point because 2.5 is not an integer.

Method you can reuse

  1. 1Look at the x-coordinate.
  2. 2Look at the y-coordinate.
  3. 3Check whether both are integers.
  4. 4If yes, it is a lattice point.
  5. 5If one coordinate is fractional or decimal, it is not.

Sketch it in your answer

Use graph paper and mark only the intersections of integer grid lines as lattice points.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is (4, -1) a lattice point on the graph?

Think first, then show answer
It is a lattice point because both coordinates are integers, so the point lies exactly on a grid intersection.

Common wrong answer

A common wrong answer is calling (2, 3.5) a lattice point because only the x-coordinate is integer.

Don't mix this up

Students sometimes count any marked dot as a lattice point, even if it lies between grid intersections.

Exam tip

Check both coordinates. One integer is not enough; both must be integers.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Identify lattice points from a list, count them on a graph, or use them while plotting coordinates in a diagram-based question.
  1. 1

    Enough for 1 mark

    A lattice point is a point whose coordinates are both integers.

  2. 2

    Add for 2 marks

    Example: (4, -1) is a lattice point, but (2, 3.5) is not.

  3. 3

    Add for 3 marks

    Lattice points are the clean grid points on graph paper, where both x and y are whole numbers or integers.

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