There is no escape...believe it or not. Mathematics is everywhere.
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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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