Let A(h, k), B(1, 1) and 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 'k' can take is given by

Options

A. `{1,3}`
B. `{0,2}`
C. `{-1,3}`
D. `{-3,-2}`

Answer

C

Explanation

Since ordinates of B and C are same. So BC is parallel to x-axis . Also, `angleCB=90^(@)` . Therefore, BA is prallele to y-aixs. So, x-coordinate of A is 1 i.e., h=1

Now, Area of `DeltaABC=1` sq. unit
`rArr(1)/(2)BCxxAB=1`
`rArr (1)/(2)xx1xx|k-1|=1`
`rArr |k-|=2 rArr k-1=+-2 rArr k=-1,3`