The midpoint 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.
For P(x,y)
X = (– 10 – 2)/2 = – 6
Y = (4 + 0)/2 = 2
Thus, P(– 6,2)
Now
– 6 = (m1x2 + m2x1)/ m1 + m2
– 6 = (m1(– 4) + m2(– 9))/ m1 + m2
– 6 = (– 4m1 – 9m2)/ m1 + m2
– 6(m1 + m2) = – 4 m1 – 9 m2
– 2m1 = – 3m2
m1:m2 = 3:2,
2 = (m1y2 + m2y1)/ m1 + m2
2 = (3 × y + 2x (– 4))/5
2 = (3y – 8)/5
10 = 3y – 8
3y = 18
y = 6