Question

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

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

Answer 1

The correct option is C {-1, 3}

Since, A(h, k), B(1, 1) and C (2, 1) are the vertices of a right angled $\Delta ABC$.

Now, area of $\Delta ABC$
$=\frac{1}{2}|k-1|.1$
$\Rightarrow 1=\frac{1}{2}|k-1|$
$\Rightarrow k-1=\pm 2$
$\Rightarrow k=-1,3$