KVPY SX SB Exam 2013 Question Paper

Question : 6 of 120

Marks: +1, -0

Consider a triangle ABC in the xy -plane with vertices A = (0,0), B = (1, 1) and C = (9, 1). If the line x = a divides the triangle into two parts of equal area, then a equals

Validate

Solution:

area of PQC =

1/2

area of ABC

1/2(9-a)(1-a/9)=1/2×1/2(8×1)

(9 - a)^2 = 36 ⇒ a = 3

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