Question

Find the coordinates of points of trisection of the line segment joining the point (6, -9) and the origin.
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Answer 1

Given:

Two points of trisection of the line segment joining the point (6, -9) and the origin.

To find:

The coordinates of points

Solution:

We have given the line segment joining the points (6, -9) and (0,0) is trisected by two points,

Let us consider the points as A(a, b) and B(c,d) which trisects the line,

The points trisect the line that means the ratio of the length of the three parts of the line will be 1:1:1

Let us take point A(a,b)

where the ratio of the intersection will be 1:2

then the coordinates of the point are given by

a = $\frac{1.0+2.6}{2+1}$

a= $\frac{13}{3}$

b = $\frac{1.0+2.(-9)}{2+1}$

b=  $\frac{-18}{3}$

b = -6

So, the coordinates of point A will be (13/3, -6)

Let us take point B(c, d)

where the ratio of the intersection will be 2:1

then the coordinates of the point are given by

c = $\frac{2.0+1.6}{1+2}$

c = $\frac{6}{3}$

c = 2

d = $\frac{2.0+1.(-9)}{2+1}$

d = $\frac{-18}{3}$

d = -6

So, the coordinates of point B will be (2, -6)