In what ratio, the line joining (– 1, 1) and (5, 7) is

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In what ratio, the line joining (– 1, 1) and (5, 7) is divided by the line x + y = 4 ?

Let the ratio be k : 1

Using internal section formula,

x =	5k - 1	= 0
	k + 1

y =	7k + 1	= 0
	k + 1

Putting the value of x and y in given equation 2x + y = 4

2		5k - 1		+	7k + 1	= 4
		k + 1			k + 1

10k – 2 + 7k + 1 = 4 (k + 1)
17k – 1 = 4k + 4
13k = 5

k =	5	= 0
	13

∴ The ratio is 5 : 13