Coordinate geometry

Asked by Abhijeetoo7 | 11th Feb, 2010, 02:40: AM

Expert Answer:

Let's label, A(-1,2), B(2,5) and C(5,8).

Also assume the three points are collinear and any one of them divides the line joining other two in the ratio m:n.

Let's say B is that point.

Using section's formula, for x coordinate,

2 = (5m-n)/(m+n)

2 = (5m/n - 1)/(m/n + 1)

This gives m/n = 1

Now for y coordinate,

5 = (8m/n + 2)/(m/n + 1)

This also gives m/n = 1.

Hence this shows that point B is on line AC and divides it in the ratio 1:1.

Therefore they are collinear.

Regards,

Team,

TopperLearning.

Answered by  | 12th Feb, 2010, 05:49: PM

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