In what ratio is the line segment joining the points A(– 2, – 3) and B(3, 7) divided by the y – axis? Also, find the coordinates of the point of division.
The segment is divided by y – axis i.e the coordinates are (0,y)
0 = (m1x2 + m2x1)/ m1 + m2
0 = (m1 × 3 + m2 (– 2))/ m1 + m2
0 = (3m1 – 2m2 ) / m1 + m2
3m1 – 2m2 = 0
m1 = 2
m2 = 3
(2:3)
y = (m1y2 + m2y1)/ m1 + m2
y = (m1 × 7 + m2(– 3))/ m1 + m2
y = (7m1 – 3m2 ) / m1 + m2
7m1 – 3m2 = y(m1 + m2)
Putting the values of m1 and m2
y = 1