Answer:
dilation by a factor of -1/2 about the center (6, 5)
(x, y) ⇒ (9 -x/2, 7.5 -b/2)
Step-by-step explanation:
Figure B is half the size of Figure A. It has been rotated, and translated. The single transformation must have all of these effects.
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rotation
The orientation of shape B is the same as that of shape A. The small extension from the rectangle still points counterclockwise relative to the figure's center. However, it points west instead of east, signifying a rotation of 180°. The same 180° rotation can be accomplished by a reflection across a point.
dilation
Shape B has half the dimensions of shape A. That means it has been dilated by a factor of 1/2. The reflection across a point can be accomplished by using a negative dilation factor.
center
The center of the dilation must reside between the two figures in order for "reflection across a point" to be accomplished. Each point on figure A must be twice as far from that center as the corresponding point on figure B.
Corresponding points are (1, 1) on figure A, and (8.5, 7) on figure B. The center of dilation divides the line between these points into the ratio 2:1. That center can be found as ...
(a, b) = (2(8.5, 7) +(1, 1))/3 = (17+1, 14+1)/3 = (6, 5)
single transformation
The single transformation that maps figure A to figure B is ...
dilation by a factor of -1/2 about the center (6, 5)
(x, y) ⇒ (9 -x/2, 7.5 -b/2)
