Question

If the point P(6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio.

Solution:

Point P divides segment AB in the ratio m : n.

A(8, 9) = (x₁, y₁), B(1, 2) = (x₂, y₂) and P(6, 7) = (x, y)

Using Section formula of internal division,

∴ `7 = (m(square) - n(9))/(m + n)`

∴ 7m + 7n = `square` + 9n

∴ 7m – `square` = 9n – `square`

∴ `square` = 2n

∴ `m/n = square`

Answer 1

Point P divides segment AB in the ratio m : n.

A(8, 9) = (x₁, y₁), B(1, 2) = (x₂, y₂) and P(6, 7) = (x, y)

Using Section formula of internal division,

`y = (my_2 + ny_1)/(m + n)`

∴ \[7 = \frac{m(\boxed{2}) - n(9)}{m + n}\]

∴ 7m + 7n = \[\boxed{2\text{m}}\] + 9n

∴ 7m – \[\boxed{2\text{m}}\] = 9n – \[\boxed{7\text{n}}\]

∴ \[\boxed{5\text{m}}\] = 2n

∴ \[\frac{m}{n} = \boxed{\frac{2}{5}}\]