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Question
Points A, B, C and D divide the line segment joining the point (5, –10) and the origin in five equal parts. Find the co-ordinates of B and D.
Solution
Point A divides PO in the ratio 1 : 4.
Co-ordinates of point A are:
`((1 xx 0 + 4 xx 5)/(1 + 4),(1 xx 0 + 4 xx (-10))/(1 + 4))`
= `(20/5, (-40)/5)`
= (4, –8)
Point B divides PO in the ratio 2 : 3.
Co-ordinates of point B are:
`((2 xx 0 + 3 xx 5)/(2 + 3),(2 xx 0 + 3 xx (-10))/(2 + 3))`
= `(15/5, (-30)/5)`
= (3, –6)
Point C divides PO in the ratio 3 : 2.
Co-ordinates of point C are:
`((3 xx 0 + 2 xx 5)/(3 + 2),(3 xx 0 + 2 xx (-10))/(3 + 2))`
= `(10/5, (-20)/5)`
= (2, –4)
Point D divides PO in the ratio 4 : 1.
Co-ordinates of point D are:
`((4 xx 0 + 1 xx 5)/(4 + 1),(4 xx 0 + 1 xx (-10))/(4 + 1))`
= `(5/5, (-10)/5)`
= (1, –2)
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