# Calculate the coordinates of the point P which divides the line joining A(-1,3), B(5,9) in the ratio 1:2.

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by aditya913

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by aditya913

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We can do by three methods.

**One:** By writing the formula for distance between two points AP(x,y) and PB and equating their ration to 1:2. Difficult calculations.

__Two :__ By shifting the origin to A(-1,3). Then A' in new coordinate system is (0,0). B' will be (6,6). P' will be (2,2) dividing A'B' by 1:2. So P will be (2-1,2+3) =** (1,5).**

__three:__ By using scalation / scaling method. Ratio to divide AB: 1:2 or 1/3 : 2/3

P( x , y ) : x = -1 **2/3* + 5 * **1/3 ** = 3/3 = 1

y = 3 ***2/3** + 9 * **1/3 =** 15/3 = 5

**Answer is (1,5)**

P( x , y ) : x = -1 *

y = 3 *