Question

Find the coordinates of the orthocentre of triangle whose vertices are (-1,3),(2,-1)and (0,0)

Answer 1

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Answer 2

Orthocenter = (-4 , -3) of triangle whose vertices are (-1,3),(2,-1)and (0,0)

Step-by-step explanation:

A - (-1 , 3)  , B (2 , - 1)  & C = (0 , 0)

AD ⊥ BC   &  BE ⊥ AC

AD & BE inetersect at orthocenter

Slope of BC =  ( 0 -(-1))/(0-2) = -1/2

Slope of AD = -1/(-1/2) = 2

AD is y = 2x + c

Passes through A

3 = 2(-1) + c

=> c = 5

AD is y = 2x + 5

Slope of AC = (0 - 3)/(0 - (-1))  = - 3

Slope of BE = -1/(-3) = 1/3

BE is  y = x/3 + c

Passes through B (2 , -1)

-1 = 2/3 + c

=> c = -5/3

y = x/3 - 5/3

y = (x - 5)/3

2x + 5 = (x - 5)/3

=> 6x + 15 = x - 5

=> 5x = -20

=> x = -4

y = (-4 - 5)/3 = -3

Orthocenter = (-4 , -3)

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