Question

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

Explanation:

Step1: Recall Reflection Over x - axis

When a figure is reflected across the \(x\) - axis, the \(y\) - coordinate of each point \((x,y)\) changes its sign, i.e., \((x,y)\to(x, - y)\). So, the figure should be a mirror image below the \(x\) - axis (if the original is above) or above (if the original is below) with respect to the \(x\) - axis.

Step2: Analyze Figure T and Options

• Figure T is above the \(x\) - axis. We need to find the figure that is the mirror image of T across the \(x\) - axis.
• Figure U: It is a reflection across the \(y\) - axis (since the \(x\) - coordinates change sign, \(x\to - x\) for reflection over \(y\) - axis), not \(x\) - axis.
• Figure V: Let's check the coordinates. For points in T, when we reflect over \(x\) - axis, the vertical position ( \(y\) - value) flips. Figure V has the same shape as T but is below the \(x\) - axis, which matches the reflection over \(x\) - axis.
• Figure W: It does not match the reflection over \(x\) - axis (it seems to be a combination of reflection and other transformations or not a reflection over \(x\) - axis).

Answer:

Figure V