the line segment joining the points (3,−4) and (1,2) is trisected at the points P and Q if the coordinates of P and Q are (p,−2) and (5/3,q) respectively find the values of p and q.


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Question Number 24179 by gopikrishnan005@gmail.com last updated on 14/Nov/17

$t h e l i n e s e g m e n t j o i n i n g t h e p o i n t s (3, - 4) a n d (1, 2) i s t r i s e c t e d a t t h e p o i n t s P a n d Q i f t h e c o o r d i n a t e s o f P a n d Q a r e (p, - 2) a n d (5 / 3, q) r e s p e c t i v e l y f i n d t h e v a l u e s o f p a n d q .$
	Answered by mrW1 last updated on 14/Nov/17

	$\frac{x_{1} - 3}{1 - 3} = \frac{1}{3}$ $\Rightarrow x_{1} = 3 - \frac{2}{3} = \frac{7}{3}$ $\frac{y_{1} - (- 4)}{2 - (- 4)} = \frac{1}{3}$ $\Rightarrow y_{1} = 2 - 4 = - 2$ $\frac{x_{2} - 1}{3 - 1} = \frac{1}{3}$ $\Rightarrow x_{2} = 1 + \frac{2}{3} = \frac{5}{3}$ $\frac{y_{2} - 2}{- 4 - 2} = \frac{1}{3}$ $\Rightarrow y_{2} = 2 - 2 = 0$ $\Rightarrow p = \frac{7}{3}$ $\Rightarrow q = 0$
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