If an triangle ABC, A≡(1$$,$$10),circumcentre ≡$$($$−$$1/3$$, $$2/3)$$, and orthocentre ≡$$($$−$$11/3$$, $$4/3)$$, then the coordinates of the midpoint of the side opposite to A are

Question

If an triangle ABC, A≡(1$$,$$10),circumcentre ≡$$($$−$$1/3$$,  $$2/3)$$, and orthocentre ≡$$($$−$$11/3$$,  $$4/3)$$, then the coordinates of the midpoint of the side opposite to A are

Infinity Learn · Accepted Answer

Circumcentre O≡$$($$−$$1/3$$,$$2/3)$$ and orthocenter H≡(11/3$$,$$4/3) Therefore, the coordinates of G are (1$$,$$8/9). Now, the point A is (1$$,$$10) as G is (1/$$ $$8/9).Also, AD : DG $$=3$$:$$1$$∴    D≡(3$$−$$13$$−$$1$$,$$8/3$$−$$103$$−$$1)≡(1$$,$$11/3)∴    $$D=(3$$−$$12)=1$$, $$Dy=(8/3)$$−$$102=$$−$$113Hence$$, the coordinates of t'he midpoint of BC are (1$$,$$-11$$ $$/3).

If an triangle $ABC, A \equiv (1, 10),$ circumcentre $\equiv (- 1 / 3, 2 / 3),$ and orthocentre $\equiv (- 11 / 3, 4 / 3),$ then the coordinates of the midpoint of the side opposite to A are

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If an triangle ABC, A≡(1,10),circumcentre ≡(−1/3, 2/3), and orthocentre ≡(−11/3, 4/3), then the coordinates of the midpoint of the side opposite to A are

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If an triangle $ABC, A \equiv (1, 10),$ circumcentre $\equiv (- 1 / 3, 2 / 3),$ and orthocentre $\equiv (- 11 / 3, 4 / 3),$ then the coordinates of the midpoint of the side opposite to A are