Let , , be the vertices of a right-angled triangle with as its hypotenuse. If the area of the triangle is , then the set of values which can take is given by
Explanation for the correct answer:
Finding the set values for :
Given , , be the vertices of a right-angled triangle.
Using the distance formula to find and
Given that the area of the triangle is
Squaring both sides
Therefore,
Hence, option (C) is the correct answer.