Question

figure e figure d a translation 5 units left and 2 units up a reflection over the x -axis a translation 2 units left and 5 units up a reflection over the y -axis

Explanation:

Step1: Analyze translation rules

Translation rules: (x,y)→(x - a,y + b) for left - a units and up b units. For option A (5 units left and 2 units up), the rule is (x,y)→(x - 5,y + 2), for option C (2 units left and 5 units up), the rule is (x,y)→(x - 2,y + 5). These do not match the transformation from Figure D to Figure E.

Step2: Analyze reflection rules

Reflection over the x - axis: (x,y)→(x, - y). Reflection over the y - axis: (x,y)→(-x,y). When we reflect a figure over the y - axis, the x - coordinates of all points change their signs while the y - coordinates remain the same. Observing Figure D and Figure E, we can see that the x - coordinates of the vertices of Figure D have their signs changed to get the vertices of Figure E, which is consistent with a reflection over the y - axis.

Answer:

D. A reflection over the y -axis