Question

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

Explanation:

Step1: Recall reflection rule

When reflecting a point \((x,y)\) across the \(x -\)axis, the rule is \((x,y)\to(x, - y)\). This means the \(x -\)coordinate remains the same and the \(y -\)coordinate changes its sign.

Step2: Analyze the figures

• For Figure \(U\): It is a reflection across the \(y -\)axis (since \((x,y)\to(-x,y)\)).
• For Figure \(V\): If we consider the vertical position of the points of Figure \(T\) and Figure \(V\), for each point \((x,y)\) in Figure \(T\), the corresponding point in Figure \(V\) has the same \(x\) - coordinate and \(y\) - coordinate with the opposite sign. For example, if a point in \(T\) is \((- 3,3)\), a corresponding point in \(V\) is \((-3,-3)\).
• For Figure \(W\): It has both \(x\) and \(y\) coordinates changed in a non - reflection - across - \(x\) - axis way.

Answer:

Figure \(V\)