Question

which figure shows a reflection of figure t across the x - axis? figure u figure v figure w

Explanation:

Step1: Understand the reflection rule

When a figure is reflected across the \(x -\)axis, the \(x -\)coordinate of each point remains the same, and the \(y -\)coordinate is multiplied by \(- 1\). This means that the figure is flipped vertically over the \(x -\)axis.

Step2: Analyze the figures

• Figure \(U\): It is not a reflection across the \(x -\)axis. If we consider the \(y -\)coordinates of the points of figure \(T\) and \(U\), they do not follow the \(y\to - y\) rule (it is more of a translation).
• Figure \(V\): For each point \((x,y)\) in figure \(T\), the corresponding point in figure \(V\) has coordinates \((x, - y)\). This satisfies the rule of reflection across the \(x -\)axis.
• Figure \(W\): It is not a reflection across the \(x -\)axis. If we check the \(y -\)coordinates of the points of figure \(T\) and \(W\), the transformation is more complex than a simple \(y\to - y\) reflection across the \(x -\)axis (it is a combination of translation and other non - reflection transformations in the \(y -\)direction).

Answer:

Figure \(V\)