Class 10 Mathematics – Distance Formula

1. What is Distance in Coordinate Geometry?

• Distance refers to the length of the straight line connecting two points in a plane.

• It helps determine how far apart two points are.

• Distance is always a positive quantity.

2. Conceptual Understanding

• Think of a line connecting two points like a rope stretched between two spots on a map.

• The length of the rope represents the distance between the points.

• The longer the rope, the greater the distance; the shorter the rope, the smaller the distance.

3. Steps to Find Distance Between Two Points

1. Identify the two points on the coordinate plane.

2. Draw a straight line connecting the points.

3. Observe the horizontal and vertical separation between the points.

4. Conceptually, combine the horizontal and vertical distances to get the straight-line distance.

4. Applications of Distance Concept

• Measuring the length of sides of triangles, rectangles, and other shapes.

• Finding the shortest path between two locations on a map.

• Verifying whether a triangle is right-angled using side lengths.

• Checking collinearity of points in combination with distance and midpoint concepts.

5. Key Points to Remember

• Distance is always positive; it cannot be negative.

• The concept is useful in geometry, coordinate geometry, and real-life measurements.

• Distance helps in solving problems related to shapes, lengths, and alignment.

• Combining distance with midpoint or section concepts helps in complex geometry problems.