**Q) P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.**

**Ans: **

**Step 1:** Given that point point R divides line PQ, so that PR = 2 QR

therefore, Point R divides the lines PQ in ratio of 2: 1

**Step 2: **By section formula, coordinates of point P (X, Y), which divides line made by two points (x_{1}, y_{1}), (x_{2}, y_{2}) in ratio of m: n, are given by:

P (X,Y) =

Now we have, X_{1} = – 2, Y_{1} = 5, X_{2} = 3, Y_{2} = 2, m_{1}= 2 and m_{2} = 1

∴ Coordinate X of point R =

∴ X =

∴ X =

Similarly, Coordinate Y of point R =

∴ Y =

∴ Y =

∴ Y = 3

**Therefore, the coordinates of point R are (, 3).**

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