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Q.

Let A(p, q), B(1, 1), C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which q can take is given by

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a

{1, 3}

b

{0, 2}

c

{–1, 3}

d

{–3, –2}

answer is C.

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Detailed Solution

A(p,q),B(1,1),C(2,1) ΔABC=12|p−1q−1p−2q−1|=1 =|(p−1)(q−1)−(p−2)(q−1)|=2 =|(pq−p−q+1)−(pq−p−2q+2)|=2 =|q−1|=2⇒q−1=±2 ⇒q=3 or −1 ∴ set of values of q={−1,3}

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