Multiple choice

If the extremities of hypotenuse of a right-angled triangle are (2, 0) and (0, 2), then what is the locus of its third vertex?

  1. x2 + y2 + 2x - 2y = 0

  2. x2 + y2 - 2x - 2y = 0

  3. x2 + y2 - 2x + 2y = 0

  4. x2 + y2 + 2x + 2y = 0

  5. x2 + y2 - 4x - 4y = 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the coordinates of the third vertex be (x,y). Applying the Pythagoras theorem in the right angled triangle, we get 8 = (x-2)2 + y2 + x2 + (y-2)2 8 = x2+4-4x+y2+x2+y2+4-4y Cancelling 8, we get x2+y2-2x-2y=0 (Correct Answer)

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