Maggie graphed the image of a 90° counterclockwise rotation about vertex a of △abc. coordinates b and c of △abc are (2, 6) and (4, 3) and coordinates b’ and c’ of it’s image are (–2, 2) and (1, 4). what is the coordinate of vertex a?

  A(2, 2)

Step-by-step explanation:

I find it useful to graph the given points. The center of rotation is at the place where the perpendicular bisectors of BB' and CC' meet. That point is ...

  A =  (2, 2).

__

The graph shows you the slope of BB' is 1, so its perpendicular bisector will have a slope of -1. The midpoint of BB' is (2-2, 6+2)/2 = (0, 4). This is the y-intercept of the line, so the perpendicular bisector of BB' has equation ...

  y = -x +4

The slope of CC' is -1/3, so its perpendicular will have a slope of -1/(-1/3) = 3. The midpoint of CC' is (4+1, 3+4)/2 = (5/2, 7/2). In point-slope form the equation of the perpendicular bisector of CC' is ...

  y -7/2 = 3(x -5/2)

  2y -7 = 3(2x -5) . . . . multiply by 2

  2(-x+4) -7 = 3(2x -5) . . . substitute for y

  -2x +1 = 6x -15 . . . . .eliminate parentheses

  16 = 8x . . . . . . . . . . add 2x+15

  x = 2 . . . . . . divide by 8

  y = -2+4 = 2 . . . . from the equation for y

The intersection of the perpendicular bisectors of BB' and CC' is the center of rotation:

  A = (2, 2)