Question

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4).

• A. (−1/3,0) and (−5/3,4)
• B. (−1/3,0) and (−5/6,2)
• C. (−1/2,0) and (−5/3,2)
• D. (−1/3,0) and (−5/3,2)

Answer 1

The correct option is D

(−1/3,0) and (−5/3,2)

Let A(1, -2) and B(-3, 4) be the given points.

Let the points of trisection be P and Q. Then,

AP = PQ = QB = $\Lambda$(say).

$\therefore$ PB = PQ + QB = 2$\Lambda$ and AQ = AP +PQ = 2$\Lambda$

$\Rightarrow$ AP:PB = $\Lambda :2\Lambda$ = 1:2 and

AQ:QB = $2\Lambda :\Lambda$ = 2:1

So, P divides AB internally in the ratio 1:2 while Q divides internally in the ratio 2:1. Thus, the coordinates of P and Q are

$P^{(\frac{1\times (-3)+2\times 1}{1+2},\frac{1\times 4+2\times (-2)}{1+2})}$ = $P^{(-\frac{1}{3},0)}$

$Q^{(\frac{2\times (-3)+1\times 1}{2+1},\frac{2\times 4+1\times (-2)}{2+1})}$ = $Q^{(-\frac{5}{3},2)}$ respectively

Hence the two points of trisection are $(-\frac{1}{3},0)$ and $(-\frac{5}{3},2)$