a changeable straight line going the point (a,b) creates a triangle with axes. what is the equation of locus of centroid of the triangle


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Question Number 121418 by deleteduser12 last updated on 08/Nov/20

$a c h a n g e a b l e s t r a i g h t l i n e g o i n g t h e p o i n t (a, b)$ $c r e a t e s a t r i a n g l e w i t h a x e s . w h a t i s$ $t h e e q u a t i o n o f l o c u s o f c e n t r o i d o f$ $t h e t r i a n g l e$
	Answered by TANMAY PANACEA last updated on 08/Nov/20

	$l e t t h e e q n b e$ $\frac{x}{p} + \frac{y}{q} = 1 \to s t l i n e m e e t x a x i s a t (p, 0) y a x i s$ $a t (0, q)$ $c e n t r o i d = (\frac{p + 0 + 0}{3}, \frac{0 + q + 0}{3}) = (\frac{p}{3}, \frac{q}{3})$ $s a y α = \frac{p}{3} β = \frac{q}{3}$ $n o w s t l i n e \frac{x}{p} + \frac{y}{q} = 1 p a s s e s t h r o u g h (a, b) s o$ $\frac{a}{p} + \frac{b}{q} = 1$ $\frac{a}{3 α} + \frac{b}{3 β} = 1$ $s o t h e l o c u s i s \frac{a}{3 x} + \frac{b}{3 y} = 1$ $\frac{a}{x} + \frac{b}{y} = 3$
	Commented by peter frank last updated on 08/Nov/20

	$thank you$
	Commented by TANMAY PANACEA last updated on 08/Nov/20

	$m o s t w e l c o m e$
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