Question

Orthocentre of a Triangle with vertices (0,0) (3,4) and (4,0) is ?


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Answer 1

Heya,

Please see the attachment for your solution..

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Answer 2

triangle ABC ', vertices are A(,4) , B (0,0) ,C (4,0)

O is the orthocentre triangle


By considering the coordinates of B ,C,A we can cinclude that :
Equation of BC is y=0 .......(1)
equation of AD is x=3 ......(2)

As we know slope of BBC (begin in on the x axis)=0

and for a vertical line AD however the slope is not defined. it does not have a slope


we take the slope of AC = (4-0)/(3-4)=4/-1=-4

So the slope of its perpendicular BE has to be its negative reciprocal . that is the slope of the= 1/4

So equation of bird which is passing through (0,0) has to be y= mx + b , where m <= 1/4 ,x=0 , y =0

0=1/4*0+b

b=0

So ,BE is y =1/4*x+0

y=x/4

now by solving


x=3.........(1)



y=x/4...........(2)

we get y= 3/4



So orthocenter coordinate are (3,3/4)


i hope its help you
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