Question

Find the co-ordinates of the point P which divides the line segment joining A (−3, 3) and B (2, −7) internally in the ratio 2 : 3.

Answer 1

Section formula:

The coordinates of the point dividing internally the line segment joining P(x1,y1) and Q(x2,y2) in the ratio m1:m2 are,

(x, y) = `((m1 xx x2 + m2 xx x1) / (m1 + m2)), ((m1 xx y2 + m2 xx y1) / (m1 + m2))`

Here,

A = (−3, 3),

B = (2, −7),

Ratio = 2 : 3 (AP : PB = 2 : 3)

Identify the values:

x1 = −3, y1 = 3;

x2 = 2, y2 = −7;

m1 = 2, m2 = 3

Apply the formula for the x-coordinate:

x = `((m1 xx x2) + (m2 xx x1)) / (m1 + m2)`

= `(2 xx 2 + 3 xx (−3)) / (2 + 3)`

= `(4 − 9) / 5`

= `−5 / 5`

= −1

Apply the formula for the y-coordinate:

y = `((m1 xx y2) + (m2 xx y1)) / (m1 + m2)`

= `(2 xx (−7) + 3 xx 3) / 5`

= `(−14 + 9) / 5`

= `−5 / 5`

= −1

Hence, the co-ordinates of the point P which divides the line segment joining are (−1, −1).