Question

Find the coordinates of the point which divides the line segment joining the points P(–1, 1) and Q(5, –7) in the ratio 2 : 3.

Answer 1

1. Identify the given values

The points are P(x₁, y₁) = (–1, 1) and Q(x₂, y₂) = (5, –7).

The given ratio is m : n = 2 : 3.

2. Apply the section formula

The section formula for internal division of a line segment is given by:

`P(x, y) = ((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`

3. Calculate the x-coordinate

Substitute the values into the formula for x:

`x = (2(5) + 3(-1))/(2 + 3)`

= `(10 - 3)/5`

= `7/5`

= 1.4

4. Calculate the y-coordinate

Substitute the values into the formula for y:

`y = (2(-7) + 3(1))/(2 + 3)`

= `(-14 + 3)/5`

= `(-11)/5`

= –2.2

The coordinates of the point which divides the line segment joining P(–1, 1) and Q(5, –7) in the ratio 2 : 3 are 1.4, –2.2 or in fraction form `(7/5, -11/5)`.