Q1) Prove that the points (a,0),(b,0), and (1,1) are collinear if 1/a + 1/b =1

Q2) Prove that the points (a,b), (c,d), and ( a-c,b-a) are collinear if ad=bc.

Q3) three consecutive vertices of a parallelogram ABCD are A (1,2) B (1,0) and C (4,0).Find the fourth vertex.

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**1.** If the question is like:

Prove that the points (*a*, 0), (0, *b*) and (1, 1) are collinear if , then the solution is:

Let A (*a*, 0), B (0, *b*) and C (1, 1) be the given points.

Suppose all given points are collinear.

∴ Area of ∆ABC = 0

⇒ *ab* – *a* – *b* = 0

Dividing both sides by *ab*, we get

Hence the given points are collinear only if when .

**3.**

Let the vertex of point D are (*x*, *y*).

Since the diagonals of a parallelogram, bisect each other, therefore co-ordinates of mid-point of AC = co-ordinates of mid-point of BD

On comparing equation, we get

⇒ *x* + 1 = 5 and *y* = 2

⇒ *x* = 4 and *y* = 2

Therefore the vertex of point D are (4, 2).

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