Question

find the coordinates of the points of trisection of the line segment joining the points a(2,-2) and b(-7,4)​

Answer 1

We have to find the coordinates of the points of trisection of the line segment joining the points a(2, -2) and b(-7,4).

Solution : trisection means three equal parts. The line joining the points a and b divides into three equal parts.

See below,

a(2, -2) .............C...........D............b(-7,4)

there C and D are two points by which line is divided into three equal parts.

if we consider C,

Then, aC : Cb = 1 : 2

Now applying section formula,

C = [(1 × -7 + 2 × 2)/(1 + 2), (1 × 4 + 2 × -2)/(1 + 2)]

= (-1, 0)

Similarly, we consider D as a reference.

Then, aD : Db = 2 : 1

Now D = [(2 × -7 + 1 × 2)/(2 + 1), (2 × 4 + 1 × -2)/(2 + 1)]

= (-4, 2)

Therefore the points are (-1,0) and (-4,2) of trisection of line joining the points a(2,-2) and b(-7,4)