Question

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3)

Options

• 1 : 2

• 2 : 1

• 1 : 3

• 3 : 1

Answer 1

1 : 3

Explanation;

Hint:

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"))`

(1, 6) = `((-2"m" + 2"n")/("m" + "n"), (3"m" + 7"n")/("m" + "n"))`

= `(-2"m" + 2"n")/("m" + "n")` = 1

−2m + 2n = m + nx

−3m = n – 2n

3m = n

`"m"/"n" = 1/3`

∴ m : n = 1 : 3

and

`(3"m" + 7"n")/("m" +  "n")` = 6

3m + 7n = 6m + 6n

6m – 3n = 7n – 6n

3m = n

`"m"/"n" = 1/3`