A line divides internally in the ratio m : n
The point P = `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`
x1 = −3, x2 = 4, y1 = 5, y2 = −9
(2, −5) = `((4"m" - 3"n")/("m" + "n"), (-9"m" + 5"n")/("m" + "n"))`
`(4"m" - 3"n")/("m" + "n")`
= 2
4m – 3n = 2m + 2n
4m – 2m = 3n + 2n
2m = 5n
`"m"/"n" = 5/2`
m : n = 5 : 2
The ratio is 5 : 2.
and
`(-9"m" + 5"n")/("m" + "n")`
= −5
−9m + 5n = −5(m + n)
−9m + 5n = −5m – 5n
−9m + 5m = −5n – 5n
−4m = −10
`"m"/"n" = 10/4`
⇒ `"m"/"n" = 5/2`
m : n = 5 : 2