Given A(-1,2) , B(-3,4) and C(-2,5) are the vertices of a triangle.
Let us find new coordinates after translating by (4,4)
New coordinates are A(-1+4,2+4), B(-3+4,4+4) and C(-2+4,5+4)
= A(3,6),B(1,8) and C(2,9)
Now it is rotated counterclockwise around A(3,6). That means A remains same and we need to find new coordinates of B and C. To find B and C let us make origin as A and find B ,C coordinates from it.
B'= (1-3,8-6) = (-2,2)
C'=(2-3,9-6)=(-1,3)
Now B' anc C' are rotated 90 degrees counter clockwise about origin. Hence (x,y) becomes (-y,x).
Hence B'(-2,2) becomes (-2,-2) and C'(-1,3) becomes (-3,-1).
Now let us move origin from (3,6) to (0,0) again.
Hence new coordinates of B are (-2+3,-2+6) = (1,4)
And new coordinates of C are (-3+3,-1+6) = (0,5)
Coordinates of triangle till translation and rotation are A(3,6) B(1,4) and C(0,5).
Now it is reflected over x-axis which means x-coordinate changes its sign.
Hence new coordinates of triangle after reflection over x-axis = A(-3,6),B(-1,4) and C(0,5)
