Distance between the circumcentre and the Orthocentre of a triangle whose vertices are (0,0),(6,8) ,(-4,3) is
Answers
Given : a triangle whose vertices are (0,0),(6,8) ,(-4,3)
To find : Distance between the circumcentre and the Orthocentre of a triangle
Solution:
vertices of triangle are (0,0),(6,8) ,(-4,3)
Orthocentre where altitude meets
(6,8) ,(-4,3) line slope = (3 - 8)/(-4 - 6) = -5/-10 = 1/2
Slope of altitude = - 2
Altitude equation
y - 0 = -2(x - 0)
=> 2x + y = 0
Slope (0,0) & (-4,3) = -3/4
Slope of altitude = 4/3
Altitude equation
y - 8 = (4/3) (x - 6)
=> 3y - 24 = 4x - 24
=> 3y = 4x
=> 3y = 2(2x)
=> 3y = 2(-y)
=> 5y = 0
=> x = 0
Orthocenter is (0,0)
Hence its a right angled triangle . ( right angle at 0 ,0)
Circumcenter = mid point of hypotenuse (6,8) ,(-4,3)
= (1 ,11/2)
Distance = √(1 - 0)² + (11/2-0)²
= (1/2)√125
= 5√5 / 2
Distance between the circumcentre and the Orthocentre of a triangle whose vertices are (0,0),(6,8) ,(-4,3) is 5√5 / 2
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