If a vertex of a triangle is (1$$, $$1) and the $$mid-points$$ two sides through this vertex are $$($$ $$-$$ $$1$$, $$2)$$ and $$($$ $$3$$, $$2)$$, then k centroid of the triangle, is

Question

If a vertex of a triangle is (1$$, $$1) and the $$mid-points$$ two sides through this vertex are $$($$ $$-$$ $$1$$, $$2)$$ and $$($$ $$3$$, $$2)$$, then k centroid of the triangle, is

Infinity Learn · Accepted Answer

Let ABC be the given triangle whose vertices $$areA(1$$,$$1)$$,$$Bx1$$,$$y1$$ and $$Cx2$$,$$y2$$ Let $$D($$−$$1$$,$$2)$$ and $$E(3$$,$$2)$$ be the $$mid-points$$ of AB and AC respectively. $$Thenx1+12=$$−$$1$$,$$y1+12=2$$,$$x2+12=3$$ and $$y2+12=2$$⇒ $$x1=$$−$$3$$,$$y1=3$$,$$x2=5$$ and $$y2=3Thus$$ the coordinates of the vertices of ∆ABC are A (1$$, $$1). $$B(-3$$, $$3)$$ and $$C(5$$, $$3)$$.∴ $$_Coordinates$$ of the centroid are $$1$$−$$3+53$$,$$1+3+33=1$$,$$73$$

If a vertex of a triangle is $(1, 1)$ and the mid-points two sides through this vertex are $(- 1, 2)$ and $(3, 2)$ , then $k$ centroid of the triangle, is

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If a vertex of a triangle is (1, 1) and the mid-points two sides through this vertex are ( - 1, 2) and ( 3, 2), then k centroid of the triangle, is

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If a vertex of a triangle is $(1, 1)$ and the mid-points two sides through this vertex are $(- 1, 2)$ and $(3, 2)$ , then $k$ centroid of the triangle, is