Two vertices of a triangle are (3$$, – $$2) and $$($$–$$2$$, $$3)$$ and its orthocenter is $$($$–$$6$$, $$1)$$. Then the third vertex of this triangle can NOT lie on the line

Question

Infinity Learn · Accepted Answer

Let $$m1=slope$$ $$ofBH=1$$−$$($$−$$2)$$−$$6$$−$$3=$$−$$13$$⇒Slope of $$AC=3$$ ∴Equation of AC is  y−$$3=3(x+2)$$ or  $$3x$$−$$y+9=0$$       (1)Let$$ $$m2$$ $$=$$ slope of $$CH=1$$−$$3$$−$$6+2=12$$⇒Slope of AB  $$=-2$$∴Equation of AB is $$y+2=$$−$$2(x$$−$$3)or$$ $$2x+y$$−$$4=0$$                                $$(2)As$$ A lies on $$(1) and (2), coordinates of A are $$($$– $$1$$, $$6)$$ and it does not lie on $$5x+y=2$$

Two vertices of a triangle are (3, – 2) and (–2, 3) and its orthocenter is (–6, 1). Then the third vertex of this triangle can NOT lie on the line

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