Question

find the ratio in which the line segment joining A(1,-5) and B(-4,5) is divided by the x-axis. Also find the co- ordinates of the point of division

Answer 1

Let the ratio be k:1, where k is the required ratio in fraction form.

Therefore m1 = k and m2 = 1.

x1 = 1, x2 = -4, y1 = -5 & y2 = 5.

The dividing point lies on the x axis. So (y = 0).

Now, we get:

x = [(k)*(-4) + 1] / (k + 1) = (-4k + 1) / (k + 1).

0 = [(k)*(5) + (-5)] / (k + 1) = (5k - 5) / (k + 1).

0 = 5k - 5. 》5k = 5 》k = 1.

Therefore the ratio is 1:1.

Now, substituting the value of k to eq. 1,

x = (-4 + 1) / (1 + 1)

x = (-3 / 2).

So the coordinates are (-3/2 , 0).

Hope it helps!