Find the ratio in which the point P 3 4 ,   5 12 divides the line segment joining the points
A 1 2 ,   3 2 and 2 , - 5 .                                        [CBSE 2015]

Let k : 1 be the ratio in which the point P34, 512 divides the line segment joining the points A12, 32 and 2,-5. Then
34,512=k2+12k+1,k-5+32k+1k2+12k+1=34   and k-5+32k+1=5128k+2=3k+3   and -60k+18=5k+5k=15   and k=15
Hence, the required ratio is 1 : 5.

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