Question

The mid-point P of the line segment joining the points A(–10, 4) and
B(–2, 0) lies on the line segment joining the points C(–9, –4) and D(–4, y).
Find the ratio in which P divides CD. Also find the value of y.

Answer 1

Mid-point P of the line segment joining A(-10, 4) and B(-2, 0) = [(-10-2) / 2, (4+0) / 2] = (-6, 2)
Let the ratio in which the point P divides the line segment joining the points C(–9, –4) and D(–4, y) be m:n.

[(-4m - 9n) / (m + n)] = -6

(-4m - 9n) = -6m - 6n

6m - 4m = 9n - 6n
2m = 3n
m/n = 3/2

m:n = 3:2

So, the ratio in which the point P divides the line segment CD is 3:2.

[(3y - 8) / (3 + 2)] = 2

(3y - 8) = 10

3y = 10 + 8
y = 18/3
y = 6.