The Co-Ordinates of the Point P dividing the line Segment Joining the Points A (1,3) and B (4,6) Internally in the Ratio 2:1 are - Bzziii

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The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6) internally in the ratio 2:1 are 

(a) (2,4) 
(b) (4,6) 
(c) (4,2) 
(d) (3,5) 




It is given that P divides the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1.
A (1,3) and B (4,6)
Thus,

Coordinates of P = (`\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}`,`\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}`)

= (`\frac{2\times4+1\times1}{2+1}`,`\frac{2\times6+1\times3}{2+1}`)

= (`"8 + 1"/3`,`"12 + 3"/3`)

= (`9/3`,`15/3`)

= (3, 5)

So, the Correct answer is option (d) (3,5) 





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