Question

Find the ratio in which the line segment joining the points A (3, -6) and B (5, 3) is divided by x-axis. Also find the co-ordinates of the point of intersection.

Answer 1

Given: P (x1, y1) and Q(x2, y2) are the points given.
To Find: The intersecting point line with x-axis.

Solution:
Let the point of intersection of line PQ with the X axis be R(x, 0) and the ratio in which the line is divided be k:1.

So, R(x, 0) = R{[(m1x2 + m2x1)/ (x1 + x2)] , [(m1y2 + m2y1)/ (y1 + y2)]}
R(x, 0) = R{[(kx2 + x1)/ (x1 + x2)] , [(ky2 + y1)/ (y1 + y2)]}

Now, 0 = [(ky2 + y1)/ (y1 + y2)]
0 = (ky2 + y1)
- y1/y2 = k
- y1:y2 = k:1
This is the correct solution
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