If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then
(A) AP = 1/3 AB (B) AP = PB (C) PB = 1/3 AB (D) AP = 1/2 AB
This question is inspired from Example 7 - Chapter 7 Class 10 - Coordinate Geometry
Last updated at Aug. 16, 2021 by Teachoo
This question is inspired from Example 7 - Chapter 7 Class 10 - Coordinate Geometry
Transcript
Question 15 If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then (A) AP = 1/3 AB (B) AP = PB (C) PB = 1/3 AB (D) AP = 1/2 AB We need to find ratio between AP & PB Let the ratio be k : 1 Also, x1 = 4, y1 = 2 x2 = 8, y2 = 4 & x = 2, y = 1 Using section formula x = (๐1 ๐ฅ2 + ๐2 ๐ฅ1)/(๐1 + ๐2) 2 = (๐ ร 8 + 1 ร 4)/(๐ + 1) 2 = (8๐ + 4)/(๐ + 1) 2(k + 1) = 8k + 4 2k + 2 = 8k + 4 2 โ 4 = 8k โ 2k โ2 = 6k 6k = โ 2 k = (โ2)/6 k = (โ๐)/๐ Since the ratio is negative, Point P divides AB externally And ratio is 1 : 3 So, our figure looks like Thus, ๐จ๐ท/๐ท๐ฉ = ๐/๐ ๐จ๐ท/(๐จ๐ท + ๐จ๐ฉ) = ๐/๐ 3AP = AP + AB 3AP โ AP = AB 2AP = AB AP = ๐/๐ AB So, the correct answer is (d)
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