Q13 of 77 Page 7

Find the ratio in which the points P (3/4, 5/12) divides the line segments joining the points A (1/2, 3/2) and B (2, - 5).

Given: Point P (3/4, 5/12), A (1/2, 3/2) and B (2, - 5)


To find: The ratio in which P divides the line.


Formula Used:


Section formula:


If point P (x, y) divides the line segment A (x1, y1) and B(x2,y2)


Then the coordinates of P are:



Explanation:


Given points are A (1/2 , 3/2) and B(2, - 5)


Let the point P (3/4, 5/12) divide AB in ratio m:n.


For point P on the line joined by the points A and B.


… (1)


And,


… (2)


Solving 1,





⇒ 3(m + n) = 8m + 2n


∴3m + 3n = 8m + 2n


∴ 5m = n



Hence, ratio is 1:5.


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