Question

find the coordinates of points which trisect the line segment joining (2,_3) and (5,6)

Answer 1

Answer:

first point is that which divides the following line segment in the ratio 2:1.

so, by section formula,

abscissa of first point is

((m2x1 + m1x2)/(m1 + m2))

= ((1×2 + 2 × 5)/(2+1))

= ( ( 2 + 10 ) / 3 )

= 12/3 = 4

ordinate of first point is

((m2y1 + m1y2)/(m1 + m2))

= ((1×-3 + 2 × 6)/(2+1))

= ( ( -3 + 12 ) / 3 )

= 9/3 = 3

so, the first point is (4,3)

second point is that which divides the following line segment in the ratio 1:2.

so, by section formula,

abscissa of second point is

((m2x1 + m1x2)/(m1 + m2))

= ((2×2 + 1 × 5)/(1+2))

= ( ( 4 + 5 ) / 3 )

= 9/3 = 3

ordinate of second point is

((m2y1 + m1y2)/(m1 + m2))

= ((2×-3 + 1 × 6)/(1+2))

= ( ( -6 + 6 ) / 3 )

= 0/3 = 0

so, the second point is (3,0)