Question

The points which trisect the line segment joining the points (0, 0) and (9, 12) are

• A. (3, 4)
• B. (8, 6)
• C. (6, 8)
• D. (4, 0)

Answer 1

Answer: (A), (C)

(3, 4)
(6, 8)

Suppose Points P and Q trisect the line segment joining the
points$A(0,0)$ and $B(9,12)$
This means, P divides AB in the ratio $1:2$ and Q divides it in the ratio
$2:1$

Using the section formula, if a
point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $m:n$, then
$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(9,12)$ and $m=1,n=2$ in the section formula, we get
the point P $=(\frac{1\left(9\right)+2\left(0\right)}{1+2},\frac{1\left(12\right)+2\left(0\right)}{1+2})=(3,4)$

Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(9,12)$ and $m=2,n=1$ in the section formula, we get the point Q $=(\frac{2\left(9\right)+1\left(0\right)}{2+1},\frac{2\left(12\right)+1\left(0\right)}{2+1})=(6,8)$