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The midpoint of a straight fence AB is M(−2, 5). One end of the fence is B(4, −1). Find the other end A.

Class 10Coordinate GeometryGeometry — Coordinates
  • A(-8, 11)
  • B(1, 2)
  • C(-8, 9)
  • D(8, -11)

Step-by-Step Solution

If is the midpoint of then ; . So = (−8, 11), and the check works: ✓. Averaging and instead of doubling gives (1, 2) — a point between them, not the far end. Writing loses the minus sign on B's -coordinate.
Answer: A) (-8, 11)

Key idea: Section formula and midpoint

**Section formula (internal)**:
A point dividing segment in ratio closer to A means smaller) has coordinates:



Where ₁, ₁), ₂, ₂).

**Midpoint** is the special case .

**Example**: Find the point dividing in ratio 2:3 where .
Point: (3, 1).

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