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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 1 square unit, then the set of values which 'k' can take is given by

1. {−1, 3}
2. {−3, −2}
3. {1, 3}
4. {0, 2}

Correct answer: {−1, 3}

Solution

The area of triangle ABC can be calculated using the formula for the area of a triangle, which is 1/2 * base * height. Given that AC is the hypotenuse, the height can be determined by the vertical distance from point B to line AC, and the base is the horizontal distance between points A and C. Solving the area equation leads to the values of k being -1 and 3.

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