In what ratio does the X - axis divide the line segment joining the points ( - 4, - 6) and ( - 1, 7)? Find the coordinates of the points of division.

Let the required ratio be λ:1

So, the coordinates of the point M of division A ( - 4, - 6) and B ( - 1, 7) are;

Here we have;

x₁ = - 4,

x₂ = - 1 and

y₁ = - 6

y₂ = 7

=

According to the question,

Line segment joining A ( - 4, - 6) and B ( - 1, 7) is divided by the X - axis.

So y - coordinate must be zero.

So, the required ratio is 6:7 and the point of division M is;

=

=

=

Hence, the point of division is