Question

Show that the line segment joining the points (–5, 8) and (10, −4) is trisected by the co-ordinate axes.

Answer 1

Let the points A (–5, 8) and B (10, −4).

Let P and Q be the two points on the axis which trisect the line joining the points A and B.

∵ AP = PQ = QB

∴ AP : PB = 1 : 2 and AQ : QB = 2 : 1

Now, co-ordinates of P will be,

`x = (1 xx 10 + 2 xx (-5))/(1 + 2)`

= `(10 - 10)/3`

= 0

y = `(1 xx (-4) + 2 xx 8)/(1 + 2)`

= `(-4 + 16)/3`

= `12/3`

= 4

∴ Co-ordinates of P are (0, 4)

Co-ordinates of Q will be,

`x = (2 xx 10 + 1 xx (-5))/(2 + 1)`

= `(20 - 5)/3`

= `15/3`

= 5

`y = (2 xx (-4) + 1 xx 8)/(2 + 1)`

= `(-8 + 8)/3`

= `0/3`

= 0

∴ Co-ordinates of Q are (5, 0)

Hence Proved.