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Intermediate △ Geometry Topic 59 of 100

Distance Formula

Distance between two points in the plane.

Key idea

Distance between two points in the plane.

In depth

Between (x₁, y₁) and (x₂, y₂), d = √((x₂ − x₁)² + (y₂ − y₁)²). It is the Pythagorean theorem applied to the horizontal and vertical differences.

Worked example

From (1, 2) to (4, 6): √(9 + 16) = 5.

Formula

d = √((x₂−x₁)² + (y₂−y₁)²)

Real-world uses

Common mistake

Forgetting to take the square root, or adding rather than squaring the differences.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Distance Formula?

Distance between two points in the plane. It is a topic at the intermediate level in Geometry.

What is the formula for Distance Formula?

The key formula is d = √((x₂−x₁)² + (y₂−y₁)²).

Where is Distance Formula used in real life?

Real-world examples: Calculating straight-line distance between two GPS points; Measuring the length of a diagonal path.

What should I learn before Distance Formula?

Make sure you are comfortable with Congruence Transformations, the previous topic in Geometry.

What is a common mistake with Distance Formula?

Forgetting to take the square root, or adding rather than squaring the differences.

How can I practise Distance Formula?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Distance Formula?

Move on to Midpoint Formula next.

Related intermediate topics in Geometry