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.

Answer 1

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)