Question

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally

Options

• 1 : 3

• 2 : 5

• 3 : 1

• 5 : 2

Answer 1

5 : 2

Explanation;

Hint:

When it cut the y-axis the point P is (0, a)

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"))`

(0, a) = `((2"m" - 5"n")/("m" + "n"), (3"m" + "n")/("m" + "n"))`

`(2"m" - 5"n")/("m" + "n")` = 0

2m – 5n = 0

⇒ 2m = 5n

`"m"/"n" = 5/2`

⇒ m : n = 5 : 2