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The point A(k, −5) is 10 units away from B(2, 3). Find the NEGATIVE value of k.

Class 10Coordinate GeometryGeometry — Coordinates
  • A-4
  • B8
  • C-6
  • D-8

Step-by-Step Solution

→ → → = ±6, so or . The question asks for the negative value, so (8 is the rejected root). Writing forgets to undo the −2; writing subtracts the 2 instead of adding it.
Answer: A) -4

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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