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Distance between two points on a plane

This concept means finding the exact separation between any two points on the coordinate plane.

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Student-friendly explanation

A point-to-point distance is not guessed from the sketch; it is calculated from the coordinate changes. If the points lie on a horizontal or vertical line, the distance is just the difference of one coordinate. In every other case, the straight-line distance is found by the distance formula.

How to write this in exams

  1. 1

    Start with the exact idea

    This concept means finding the exact separation between any two points on the coordinate plane.

  2. 2

    Then show how to use it

    1. Read both coordinates carefully. 2. Check whether one coordinate is the same. 3. Use simple subtraction for horizontal or vertical lines. 4. Otherwise use the full distance formula. 5. Simplify the answer.

  3. 3

    Add one concrete example

    The points (-2, 3) and (4, 3) lie on the same horizontal line, so their distance is 6 units.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 1 unit for points (-2, 3) and (4, 3), because students look only at the y-difference and ignore the horizontal gap.

Definition

This concept means finding the exact separation between any two points on the coordinate plane.

Example

The points (-2, 3) and (4, 3) lie on the same horizontal line, so their distance is 6 units.

Rule to remember

Use d = sqrt((x2 - x1)^2 + (y2 - y1)^2). If one coordinate is the same, the formula reduces to a simple difference along the other axis.

Memory hook

Same height means horizontal counting; same side means vertical counting.

Examples and method

Worked example

For points (-2, 3) and (4, 3), the y-values are equal. So distance = |4 - (-2)| = 6 units. No square root is needed because the segment is horizontal.

Method to apply

1. Read both coordinates carefully. 2. Check whether one coordinate is the same. 3. Use simple subtraction for horizontal or vertical lines. 4. Otherwise use the full distance formula. 5. Simplify the answer.

Diagram support

Plot both points carefully, then decide whether the segment is horizontal, vertical, or slanted before calculating.

How CBSE asks it

Find the distance between two points shown on a graph, or compare distances for triangle and quadrilateral questions.

Avoid common mistakes

Common confusion

Students sometimes use the wrong coordinate change, or they treat a horizontal or vertical line as if it were a diagonal line.

Common wrong answer

A common wrong answer is 1 unit for points (-2, 3) and (4, 3), because students look only at the y-difference and ignore the horizontal gap.

Exam tip

First check whether the points are on the same horizontal or vertical line. That can save time and reduce calculation errors.

Quick check

What is the distance between points (-2, 3) and (4, 3)?

The distance is 6 units because the y-coordinates are the same, so only the horizontal change matters.

Study the distance between two points on a plane diagram carefully

Use the labelled diagram to keep distance between two points on a plane clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of distance between two points on a plane in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on distance between two points on a plane.

Revision cue

Revise distance between two points on a plane through the labels before writing the answer.

Answer writing and exam use

1-mark answer

This concept means finding the exact separation between any two points on the coordinate plane.

2-mark answer

This concept means finding the exact separation between any two points on the coordinate plane. Use d = sqrt((x2 - x1)^2 + (y2 - y1)^2). If one coordinate is the same, the formula reduces to a simple difference along the other axis. The points (-2, 3) and (4, 3) lie on the same horizontal line, so their distance is 6 units.

3-mark answer

A point-to-point distance is not guessed from the sketch; it is calculated from the coordinate changes. If the points lie on a horizontal or vertical line, the distance is just the difference of one coordinate. In every other case, the straight-line distance is found by the distance formula. Use d = sqrt((x2 - x1)^2 + (y2 - y1)^2). If one coordinate is the same, the formula reduces to a simple difference along the other axis. For points (-2, 3) and (4, 3), the y-values are equal. So distance = |4 - (-2)| = 6 units. No square root is needed because the segment is horizontal. Find the distance between two points shown on a graph, or compare distances for triangle and quadrilateral questions. A common wrong answer is 1 unit for points (-2, 3) and (4, 3), because students look only at the y-difference and ignore the horizontal gap.
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