Question

figure q is the result of a transformation on figure p. which transformation would accomplish this? a translation 1 unit left and 2 units down; a reflection over the y -axis; a translation 2 units left and 1 unit down; a reflection over the x -axis

Explanation:

Step1: Analyze translation

Translation moves the figure without flipping. If it were a translation, the orientation of the figure would remain the same. But here, the orientation seems to change in a way that is characteristic of a reflection. So we can rule out the translation options (orange and green boxes).

Step2: Analyze reflection

• Reflection over the \(y -\)axis: When we reflect a figure over the \(y -\)axis, the \(x -\)coordinates of the points of the figure change their sign (\((x,y)\to(-x,y)\)).
• Reflection over the \(x -\)axis: When we reflect a figure over the \(x -\)axis, the \(y -\)coordinates of the points of the figure change their sign (\((x,y)\to(x, - y)\)). Looking at the general position of Figure \(P\) and Figure \(Q\) (assuming a standard coordinate - based transformation visual from the graph), a reflection over the \(y -\)axis would map Figure \(P\) to Figure \(Q\) as the left - right orientation (related to \(x -\)coordinate sign change) is consistent with a \(y -\)axis reflection.

Answer:

B. A reflection over the y - axis