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