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Coordinate Geometry

• Section formula:
2

The co-ordinates of the point P (x,y), which divides the line segment joining the points A (x1, y1) and B (x2, y2) internally in the ratio m:n, are given by:

 

P x, y=mx2+nx1m+n, my2+ny1m+n


Example: In what ratio does the point (–4, 7) divide the line segment joining the points P (–1, 1) and Q (–6, 11).

Solution:  Let the point (–4, 7) divide the line segment joining the points P (–1, 1) and Q(–6, 11) in the ratio λ : 1.
Thus, by section formula, we have:

-6λ+-1λ+1,11λ+1λ+1=-4, 7-6λ-1λ+1=-4, 11λ+1λ+1=7-6λ-1=-4λ-42λ=3λ=32

Therefore, the required ratio is 3:2.

• The mid-point of the line segment join…

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