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Asked by thakurvikramsinghh | 20 Jun, 2019, 17:51: PM
answered-by-expert Expert Answer
A(0,0), B(3,4) and C(4,0) are three vertices of triangle ABC
Slope of AB = 4/3
Slope of BC = -4 
Slope of AC = 0
Orthocentre is the point of intersection of the altitudes of a triangle
So, we will find the equations of altitudes and then their point of intersection
let AD, BE and CF be the perpendiculars on sided BC, AC and AB respectively
Slope of AD = 1/4
Slope of BE = -1/0 which is undefined
Slope of CF = -3/4
E q u a t i o n space o f space A D thin space i s space fraction numerator y minus 0 over denominator x minus 0 end fraction equals 1 fourth x minus 4 y equals 0 E q u a t i o n space o f space C F space i s fraction numerator y minus 0 over denominator x minus 4 end fraction equals negative 3 over 4 3 x plus 4 y equals 12 S o l v i n g space t h e space t w o space e q u a t i o n s space w e space g e t x equals 3 space a n d space y equals 3 over 4 H e n c e comma space t h e space o r t h o c e n t r e space i s space open parentheses 3 comma 3 over 4 close parentheses
Answered by Renu Varma | 20 Jun, 2019, 18:13: PM

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