Q.

The line x = c cuts the triangle with corners (0, 0), (1, 1) and (9, 1) into two regions. For the area of the two regions to be the same, c must be equal to_.

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answer is 3.

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Detailed Solution

Area of ΔOAB=12(1)(8)=4sq. units  Equation of OB is y=19x .  Hence point E is c,c9 . Area of the right angled triangle DEB is 2 sqaure units⇒121−c9(9−c)=2⇒(9−c)2=36⇒9−c=±6⇒c=3
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The line x = c cuts the triangle with corners (0, 0), (1, 1) and (9, 1) into two regions. For the area of the two regions to be the same, c must be equal to_.