Question

Find the co-ordinates of a point R which divides the line segment joining the points P(−2, 3) and Q(4, 7) internally in the ratio 4:7.

Answer 1

Formula (section / internal division):

If R divides PQ internally in the ratio m1:m2,

So PR : RQ = m1:m2,

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

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

Identify values:

• P(x1, y1) = (−2, 3)
• Q(x2, y2) = (4, 7)
• Ratio PR : RQ = 4:7,
  so m1 = 4, m2 = 7

Substitute into the formula:

x = `((4 xx x2) + (7 xx x1)) / (4 + 7)`

= `(4 xx 4 + 7 xx (−2)) / 11`

= `(16 − 14) / 11`

∴ x = `2/11`

y = `((4 xx y2) + (7 xx y1)) / (4 + 7)`

= `(4 xx 7 + 7 xx 3) / 11`

= `(28 + 21) / 11`

∴ y = `49/11`

Hence, the co-ordinates of a point R that divides the line segment joining the points are `(2/11, 49/11)`