- A(-1, 0)
- B(-4, 2)
- C(-2.5, 1)
- D(0, -1)
Step-by-Step Solution
The point nearer A divides AB in ratio 1:2. . Point = (−1, 0).
Answer: A) (-1, 0)
Find the point that trisects (divides into three equal parts) the segment from A(2, −2) to B(−7, 4) and is nearer to A.
Class 10Coordinate GeometryGeometry — Coordinates
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.
- **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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