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 |