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Quadrilateral ABCD is plotted on the grid. Using the distance formula for its sides and diagonals, what type of quadrilateral is it?

Class 10Coordinate GeometryGeometry — Coordinates
  • ASquare
  • BRhombus that is not a square
  • CRectangle that is not a square
  • DParallelogram with unequal adjacent sides

Step-by-Step Solution

, so all sides are equal. Diagonals: and are unequal, so ABCD is a rhombus but not a square.
Answer: B) Rhombus that is not a square

Key idea: Recognising shapes from coordinates

**Common tasks**:

- **Equilateral triangle**: all three sides equal length (use distance formula).
- **Isosceles**: two sides equal.
- **Right triangle**: side lengths satisfy Pythagoras .
- **Square**: all four sides equal AND adjacent sides perpendicular (or use diagonals: equal and bisect at right angles).
- **Rhombus**: all four sides equal but not necessarily right-angled.
- **Parallelogram**: opposite sides equal (use distance formula on all 4 sides — opposite pairs equal).
- **Rectangle**: opposite sides equal AND diagonals equal.

The procedure is always: compute side lengths via distance formula → match against the criteria for each shape.

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