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The triangle with vertices O(0, 0), P(6, 0) and Q is:

Class 10Coordinate GeometryGeometry — Coordinates
  • AIsosceles but not equilateral
  • BEquilateral
  • CRight-angled at O
  • DScalene

Step-by-Step Solution

OP = 6. OQ = . PQ = . All three sides are 6, so the triangle is equilateral. The usual slip is squaring as 9 instead of 27, which gives OQ = and the wrong verdict 'isosceles'.
Answer: B) Equilateral

Key idea: Distance formula

**Distance** between two points P₁, ₁) and Q₂, ₂):

**PQ = **

This is just the Pythagoras theorem applied to the right triangle formed with horizontal and vertical legs.

**Example**: Distance between (3, 4) and (7, 1).
= .

**Special distance from origin**: distance of from (0, 0) is .

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