The centroid of an equilateral triangle is (0$$,$$0) . If two vertices of the triangle lie on $$x+y=22$$ , then one of them will have its coordinates

Question

The centroid of an equilateral triangle is (0$$,$$0) . If two  vertices of the triangle lie on $$x+y=22$$ ,  then one of  them will have its coordinates

Infinity Learn · Accepted Answer

Let the vertices B and C lie on the given line. Then, $$OD=222=2$$ (perpendicular$$ distance from $$origin=ca2+b2) Let equation od OD be $$y=mx$$,  since slope is perpendicular to $$x+y=22$$  is $$1$$, ∴equation is $$x=y$$ solving the two equations we get D (2$$,$$2)=$$ Also, $$BD=OD$$×$$tan$$⁡$$60$$∘$$=23$$ for the coordinates of B and C . Slope of the given line is $$-1$$, slope of OD is $$1$$ ,hence angle of inclination is $$450Using$$ parametric equation of line, we get     x−$$21/2=y$$−$$21/2=$$±$$23$$ or     C≡$$(2+6$$,$$2$$−$$6) and     B≡(2$$−$$6$$,$$2+6)

$The centroid of an equilateral triangle is (0, 0) . If two vertices of the triangle lie on x + y = 2 \sqrt{2}, then one of them will have its coordinates$

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The centroid of an equilateral triangle is (0,0) . If two vertices of the triangle lie on x+y=22 , then one of them will have its coordinates

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$The centroid of an equilateral triangle is (0, 0) . If two vertices of the triangle lie on x + y = 2 \sqrt{2}, then one of them will have its coordinates$