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Given the three point A(1,1) B(2,4) C(6,2).
Can you give the length of the height going through B ?
(Give the simplest answer !)

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Let AD = x, DC = y, and BD = Z.
By the Pythagorean Theorem c = 10^.5, b = 26^.5, and a = 20^.5

This is not the "simplest" solution since it involve solving a system with squares.

This problem is about to change your point of view and refrain to go for "solving the system" :-)

Thank you for this answer. Can you get the simpler ?

I've to admit that your answer is really simple...but empty ;)

Math Chique said:

h = height wanted

length of AC = ||AC|| = sqrt(26)

h = (Area of triangle)/(1/2*||AC||)

Area of Triangle = 1/2*||cross product of AB and AC||

AB = (1,3)         AC = (5,1)

||cross product of AB and AC|| = 5*3 - 1*1 = 14,  therefore

Area of Triangle = 7

h = 7/(1/2*sqrt(26)) = (7/13)*sqrt(26)

The simplest answer only involve knowledge of Pythagoras'theorem.

(All your's are good but use advanced knowledge)  


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