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प्रश्न
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:
विकल्प
A. (2, 4)
B. (3, 5)
C. (4, 2)
D. (5, 3)
उत्तर
Let P(x, y) divides line segment joining A (1, 3) and B (4, 6) in the ratio 2 : 1.
We know that, the coordinates of a point (x, y) dividing the line segment joining the points (x1, y1) and (x2, y2) in the ratio m1 : m2 are given by
`x=(m_1x_2+m_2x_1)/(m_1+m_2)` and `y=(m_1+y_2+m_2y_1)/(m_1+m_2)`
`therefore Here x=(2(4)+1(1))/(2+1)` and `y=(2(6)+1(3))/(2+1)`
`rArrx=9/3 ` and `y=15/3`
`rArrx=3` and `y=3`
Thus, (3, 5) divides the line segment AB in the ratio 2 : 1.
Hence, the correct answer is B.
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