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Lattice point reasoning

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Grid intersection means both numbers are whole.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

It is a lattice point because both coordinates are integers, so the point lies exactly on a grid intersection.

Answer writing and exam use

1-mark answer

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

2-mark answer

A lattice point is a point whose coordinates are both integers. A lattice point has integer coordinates of the form (x, y), where x and y are both integers. (4, -1) is a lattice point, but (2, 3.5) is not.

3-mark answer

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. A lattice point has integer coordinates of the form (x, y), where x and y are both integers. (4, -1) and (-3, 2) are lattice points because both coordinates are integers. But (1, 2.5) is not a lattice point because 2.5 is not an integer. Identify lattice points from a list, count them on a graph, or use them while plotting coordinates in a diagram-based question. A common wrong answer is calling (2, 3.5) a lattice point because only the x-coordinate is integer.
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