If AD, BE and CF are the altitudes of a triangle ABC whose vertex A is the point $$(-4$$, $$5)$$. The coordinates of the points E and F are (4$$,$$1) and $$(-1$$, $$-4)$$ respectively, then equation of BC is

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Infinity Learn · Accepted Answer

Slope of $$AF=5$$−$$($$−$$4)$$−$$4+1=9$$−$$3=$$−$$3$$∴ Slope of $$CF=13$$∴ Equation of CF is x−$$3y$$−$$11=0-----(1)$$ Slope of $$AE=5$$−$$1$$−$$4$$−$$4=4$$−$$8=$$−$$12$$∴ Slope of $$BE=2$$∴ Equation of BE is $$2x$$−y−$$7=0----(2)$$ Solving (i) and (ii), we get point $$O=(2$$,−$$3)$$ Equation of AC is $$x+2y$$−$$6=0----(3)$$ Solving (i) and (iii) we get point $$C(8$$,−$$1)$$ Also slope of AO is −$$43$$∴ Slope of BC is $$34$$∴ Equation of BC is $$3x$$−$$4y$$−$$28=0$$

If AD, BE and CF are the altitudes of a triangle ABC whose vertex A is the point (-4, 5). The coordinates of the points E and F are (4,1) and (-1, -4) respectively, then equation of BC is

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