Question

Two vertices of a triangle are (0,3) and (5,4) and its orthocentre is at origin , then its third vertex is the Quadrant

Answer 1

Given :  Two vertices of a triangle are (0,3) and (5,4) and its orthocentre is at origin

To Find : third vertex is in  the Quadrant

Solution:

Let say  A  (0 . 3)

B = ( 5 , 4)

C = ( x , y )

Orthocenter   = (0 , 0)

CF  ⊥ AB

AB slope = ( 4 - 3)/(5 -0) = 1//5

Slope of CF = - 5

y  - 0 = - 5(x - 0)

=> y = -5x

Vertex C   =  ( x  , - 5x )  

AD   ⊥ BC

Slope of AD = ( 3 - 0)/(0 - 0) = 3/0

Slope of BC =  0

y - 4 = 0(x - 5)

=> y  = 4

( x  , - 5x )  

-5x = 4

=> x = -4/5  

(-4/5  ,  4 )

third vertex  = (-4/5  ,  4 )  

2nd Quadrant

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