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  4. Let A (1, 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 1square unit, then the set of values which 'k' can take is given by

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Q. Let A (1, 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 1square unit, then the set of values which 'k' can take is given by

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Solution:

Given : The vertices of a right angled triangle A(l, k), B(1, 1) and C(2, 1) and Area of $\Delta$ABC = 1 square unit
We know that, area of right angled triangle
$= \frac{ 1}{2} \times BC \times AB = 1 = \frac{1}{2}\left(1\right)\left|\left(k-1\right)\right| $
$ \Rightarrow \pm\left(k-1\right) = 2 \Rightarrow k = - 1, 3 $

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