Question

If the line segment joining the points A(3,4) and B(14,-3) meets the x-axis at P, then the ratio in which P divides the segment AB answer

Answer 1

Let m:n be the ratio in which point P divides line segment AB and let (x, y) be the coordinates of the point P.

Since P is the point of intersection of line AB with the x-axis, the y-coordinate of P equals 0.

Then, the coordinates of P is (x, 0)

now using section formula for y-coordinate of point P we have,

y = [m×(-3) + n×4]/(m+n)

=> 0 =(-3m + 4n)/(m+n)

=> 0 × (m+n) = -3m + 4n

=> -3m + 4n = 0

=> -3m = -4n

=> 3m = 4n

=> m/n = 4/3

=> m:n = 4:3

therefore the required ratio is 4:3