1.

If points (x,0),(0,y)and (1,1) are collinear then the relation between x and y is

Answer»

The answer is given below :

Since, the three points (x,0), (0,y) and (1,1) are collinear, the triangle formed by the points will have an AREA of 0 units.

Then,

| x 0 1 |
| 0 y 1 | = 0
| 1 1 1 |

⇒ x(y - 1) - 0 + 1(0 - y) = 0, expanding along the FIRST row.

⇒ XY - x - y = 0

⇒ xy = x + y

⇒ 1/x + 1/y = 1,
which is the REQUIRED relation between x and y.

Thank you for your question.


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