Question

what is the relationship between figure a and figure b? figure a figure b -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x y y 7 7 6 6 5 5 4 4 3 3 2 2 1 1 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 figure a was reflected over the y - axis. figure a was dilated by a scale factor of 2. figure a was translated left 2 units and up 4 units. figure a was translated right 4 units and up 2 units. figure a was translated right 4 units and up 2 units.

Explanation:

Step1: Analyze reflection

For a reflection over the y - axis, the x - coordinates of the points of Figure A would change their signs. But the x - coordinates of corresponding points in Figure A and B do not have opposite signs, so it's not a y - axis reflection.

Step2: Analyze dilation

If Figure A was dilated by a scale factor of 2, the distances between corresponding points and the origin would be doubled. But the shape and size relationship between Figure A and B does not match dilation by a factor of 2.

Step3: Analyze translation left 2 and up 4

If we consider a translation left 2 and up 4, the x - coordinates of points in Figure A should decrease by 2 and y - coordinates should increase by 4. This is not the case for corresponding points in Figure A and B.

Step4: Analyze translation right 4 and up 2

Take a vertex of Figure A, say the left - most vertex with coordinates (-5,-4). If we translate it right 4 units (add 4 to the x - coordinate) and up 2 units (add 2 to the y - coordinate), we get (-5 + 4,-4+2)=(-1,-2), which matches the corresponding vertex in Figure B. This is true for all vertices.

Answer:

Figure A was translated right 4 units and up 2 units.