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$If A (1, p^{2}), B (0, 1), and C (1, 0) are the coordinates of three points, then the value of p for which the area of$ $triangle A B C is the minimum is$

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a

0

b

-13

c

12

d

±2

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detailed solution

Correct option is A

The area of the traingle formed by the given points is minimum it means that the area of the triangle formed by the given points is zero hence the given points are collinear the slopes of line joining any two points are equal It gives 1-p2-1=-11 1-p2=1 p2=0 p=0

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