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Geometry
Level
2
If the coordinates of the midpoints of the side of a triangle are and . then find the coordinates of its vertices.
(3, 2), (1, 2), (1, 4)
(3, 2), (-1, 2), (1, -4)
(3, -2), (1, -2), (1, -4)
(-3, -2), (-1, -2), (-1, -4)
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Centroid of these three mid-points = centroid of original triangle
Centroid = 3 1 ( ( 1 , 2 ) + ( 0 , − 1 ) + ( 2 , − 1 ) ) = ( 1 , 0 )
Centroid cut medians into 2 : 1
The three points are
( 1 , 0 ) − 2 ( ( 1 , 2 ) − ( 1 , 0 ) ) = ( 1 , − 4 )
( 1 , 0 ) − 2 ( ( 0 , − 1 ) − ( 1 , 0 ) ) = ( 3 , 2 )
( 1 , 0 ) − 2 ( ( 2 , − 1 ) − ( 1 , 0 ) ) = ( − 1 , 2 )