A point which divides the join of A (-3, 4) and B (9, 6) internally in the ratio 3:2 is:

To find the point that divides the line segment AB internally in the ratio 3:2, we can use the section formula.

Let's assume that the point dividing AB internally is P(x, y).

According to the section formula, the coordinates of P can be calculated as follows:

x = (2 * x2 + 3 * x1) / (2 + 3) y = (2 * y2 + 3 * y1) / (2 + 3)

where (x1, y1) are the coordinates of point A (-3, 4) and (x2, y2) are the coordinates of point B (9, 6).

Plugging in the values, we get:

x = (2 * 9 + 3 * -3) / (2 + 3) y = (2 * 6 + 3 * 4) / (2 + 3)

Simplifying the equations, we have:

x = (18 - 9) / 5 y = (12 + 12) / 5

x = 9 / 5 y = 24 / 5

Therefore, the point that divides the line segment AB internally in the ratio 3:2 is P(9/5, 24/5).