# Q1) Prove that the points (a,0),(b,0), and (1,1) are collinear if 1/a + 1/b =1Q2) 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

abab = 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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