Question

vertices of a triangle are (0, 6) (6, 6) and (6, 0) The distance between its orthocentre and centroid is
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Answer 1

Given : vertices of a triangle are (0, 6) (6, 6) and (6, 0)

To Find :  The distance between its orthocentre and centroid is

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Solution:

orthocentre  - intersection of altitudes

centroid   - intersection of median

vertices of a triangle are (0, 6) (6, 6) and (6, 0)

Hence triangle is isosceles right angle triangle

so Orthocenter of triangle will lie on ( 6 , 6)

Median from ( 6 , 6)   will be at ( 3 , 3)  

Distance between ( 6 , 6) and ( 3 , 3)

= √(6 - 3)² + (6 - 3)²

= 3√2

Centroid divided median in 2 : 2 ration  from vertex side

=> Distance between vertex and centroid   = (2/3)  3√2

= 2√2

Vertex is orthocenter

Hence  distance between its ortho centre and centroid is  2√2

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