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Coordinate-based perimeter

Perimeter is the total length around the boundary of a figure drawn using coordinates.

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Student-friendly explanation

To find perimeter on a coordinate plane, calculate each side length with the distance formula and then add them all. The key idea is to walk around the outside edge, not across the figure. This concept often appears in triangle and quadrilateral questions.

How to write this in exams

  1. 1

    Start with the exact idea

    Perimeter is the total length around the boundary of a figure drawn using coordinates.

  2. 2

    Then show how to use it

    1. Find each side length. 2. Keep the sides in boundary order. 3. Add every side. 4. Simplify carefully. 5. Write the answer with units.

  3. 3

    Add one concrete example

    If a triangle has side lengths 3, 4, and 5 units, its perimeter is 12 units.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 9 units because students add only two sides or leave out one boundary length.

Definition

Perimeter is the total length around the boundary of a figure drawn using coordinates.

Example

If a triangle has side lengths 3, 4, and 5 units, its perimeter is 12 units.

Rule to remember

Perimeter = sum of all boundary side lengths. Each side can be found by the distance formula if coordinates are given.

Memory hook

Perimeter means the full walk around the shape.

Examples and method

Worked example

For a triangle with side lengths 3, 4, and 5, perimeter = 3 + 4 + 5 = 12 units.

Method to apply

1. Find each side length. 2. Keep the sides in boundary order. 3. Add every side. 4. Simplify carefully. 5. Write the answer with units.

Diagram support

Mark the vertices in order around the boundary so that no side is missed and no diagonal is counted.

How CBSE asks it

Find the perimeter of a triangle or quadrilateral from coordinates, or compare the perimeter of two shapes on a graph.

Avoid common mistakes

Common confusion

Students sometimes add coordinates or only two sides instead of adding every side around the shape.

Common wrong answer

A common wrong answer is 9 units because students add only two sides or leave out one boundary length.

Exam tip

Write the side lengths one by one in order around the figure, then add them at the end.

Quick check

A triangle has side lengths 3 units, 4 units, and 5 units. What is its perimeter?

The perimeter is 12 units because perimeter means the sum of all three side lengths: 3 + 4 + 5 = 12.

Answer writing and exam use

1-mark answer

Perimeter is the total length around the boundary of a figure drawn using coordinates.

2-mark answer

Perimeter is the total length around the boundary of a figure drawn using coordinates. Perimeter = sum of all boundary side lengths. Each side can be found by the distance formula if coordinates are given. If a triangle has side lengths 3, 4, and 5 units, its perimeter is 12 units.

3-mark answer

To find perimeter on a coordinate plane, calculate each side length with the distance formula and then add them all. The key idea is to walk around the outside edge, not across the figure. This concept often appears in triangle and quadrilateral questions. Perimeter = sum of all boundary side lengths. Each side can be found by the distance formula if coordinates are given. For a triangle with side lengths 3, 4, and 5, perimeter = 3 + 4 + 5 = 12 units. Find the perimeter of a triangle or quadrilateral from coordinates, or compare the perimeter of two shapes on a graph. A common wrong answer is 9 units because students add only two sides or leave out one boundary length.
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