Straight Lines
A point divides the line segment joining (2, -3) and (8, 9) internally in the ratio 1 : 2; what are the coordinates of this dividing point?
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- straight lines
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
(4,1)
The section formula gives the coordinates of a point dividing a segment internally in ratio m : n as ((m x_2 + n x_1)/(m + n), (m y_2 + n y_1)/(m + n)); applying it directly avoids any geometric guesswork. With (x_1, y_1) = (2, -3), (x_2, y_2) = (8, 9), and m : n = 1 : 2, the x-coordinate is (1·8 + 2·2)/(1 + 2) = (8 + 4)/3 = 12/3 = 4, and the y-coordinate is (1·9 + 2·(-3))/3 = (9 - 6)/3 = 3/3 = 1. Hence the point is (4, 1). Option (6, 5) swaps the ratio to 2 : 1. Option (5, 3) is the midpoint, valid only for ratio 1 : 1. Option (4, -1) mishandles the y-term sign of -3. This is the standard JEE Advanced internal-division computation. Plausibility check: the point (4, 1) lies between the endpoints and is closer to (2, -3), as expected when the segment nearer that end carries the smaller ratio part, confirming the placement.
This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of straight lines. It appeared in the 2025 exam.
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