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Chapter 7 · Question 1

State the distance formula between two points (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2).

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Q1

State the distance formula between two points (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2).

Answer Revealed
Direct Answer:
The distance is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.

Simple Explanation

Use the horizontal difference and vertical difference as the legs of a right triangle.

Exam-Ready Structure

The distance formula comes from Pythagoras theorem. If A(x1,y1)A(x_1,y_1) and B(x2,y2)B(x_2,y_2), then horizontal distance is ∣x2−x1∣|x_2-x_1| and vertical distance is ∣y2−y1∣|y_2-y_1|. Therefore AB=(x2−x1)2+(y2−y1)2AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.

Key Points

  • The distance is d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q2

Find the distance between (2,3)(2,3) and (6,6)(6,6).

Q3

How can the distance formula be used to test whether three points are collinear?

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