Question

Find the co-ordinates of the points of trisection of the segment joining the points A(-7,4) and B(2,-2).

• A. (-4,0)
• B. (-1,0)
• C. (-4,2)
• D. (-2,0)

Answer 1

Answer: (B), (C)

(-4,2)

Let P and Q be the points of trisection of the line segment joining the points A and B.


Point P and point Q divide the line segment AB into 3 parts.
AP = PQ = QB ........(i)

$\frac{AP}{PB}=\frac{AP}{PQ+QB}=\frac{AP}{AP+AP}=\frac{1AP}{2AP}\frac{AP}{PB}=\frac{1}{2}$
Point $P$ divides segment $AB$ in the ratio 1 : 2.

Co-ordinate of point by section formula $(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
$P(x,y)=(\frac{1\times 2+2\times (-7)}{1+2},\frac{1\times (-2)+2\times 4}{1+2})P(x,y)=(\frac{-12}{3},\frac{6}{3})=(-4,2)$

Point Q divides segment AB in the ratio 2 : 1.
Co-ordinate of point $Q(x,y)=(\frac{2\times 2+1\times (-7)}{2+1},\frac{2\times (-2)+1\times 4}{2+1})Q(x,y)=(\frac{-3}{3},\frac{0}{3})=(-1,0)$

$\therefore$ Co-ordinates of the points of trisection are $(-1,0)\&(-4,2)$.