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NDA 2025 Maths · Mathematics · Straight Lines · medium

The point which divides the line segment joining (1,2) and (4,5) externally in the ratio 2:1 is

Single correct option

The point which divides the line segment joining (1,2)(1,2) and (4,5)(4,5) externally in the ratio 2:12:1 is
  1. A. (7,8)(7,8)
  2. B. (3,4)(3,4)
  3. C. (−2,−1)(-2,-1)
  4. D. (52,72)\left(\tfrac52,\tfrac72\right)
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Answer: (A) (7,8)(7,8)

For external division, x=2(4)−1(1)2−1=7x=\frac{2(4)-1(1)}{2-1}=7 and y=2(5)−1(2)2−1=8y=\frac{2(5)-1(2)}{2-1}=8, giving (7,8)(7,8). The point (3,4)(3,4) is the internal division, (−2,−1)(-2,-1) reverses the ratio to 1:21:2, and (52,72)\left(\frac52,\frac72\right) is the midpoint.
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