An Archimedean Lemma

Geometry Level 4

Select two points A ( x 1 , y 1 ) A({x}_{1}, {y}_{1}) , B ( x 2 , y 2 ) B({x}_{2}, {y}_{2}) on the curve y = p x 2 + q x + r . y=px^2+qx+r. For which point on the curve C ( x 3 , y 3 ) C({x}_{3}, {y}_{3}) , between points A and B, is the area of triangle ABC maximum? Express

x 3 x 1 + x 2 \frac{{x}_{3}}{{x}_{1}+{x}_{2}} as a decimal.


The answer is 0.5.

Steven Zheng by Steven Zheng , 26, China

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1 solution

Michael Mendrin
Jul 22, 2014

I think you need to specify that points A, B are values for x, and that point C is between A, B. Otherwise, the area of triangle ABC can be infinity. And then of course we have a problem when A+B=0.

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Thanks for noticing.

Steven Zheng - 6 years, 10 months ago

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