Rotation of a triangle

Question

Rotate the triangle having vertices at (0,3) (2,4) (2,6) at 180 degrees at (2,4)... What will be the new coordinates of the triangle after rotation...  I want to know how to do it...

Answer 1

obviously the pivot point does not change.

 

for the other two vertices of the triangle, the pivot point must be the midpoint between the old vertex and the new vertex after the rotation

 

therefore point (2,6) changes to (2,2)

and point (0,3) changes to (4,5)

Answer 2

From the point of rotation at (2,4), 

 

each x, y coordinate difference to (0,3) is,  x: 2-0=2, y: 4-3=1

Adding the difference to the point of rotation, new coordinate (4, 5)

 

each x, y coordinate difference to (2,6) is, x: 2-2=0, y: 4-6=-2

Adding the difference to the point of rotation, new coordinate (2, 2)