Question

which two transformations performed in sequence on figure 1 will show figure 1 is congruent to figure 2? move two transformations to the first transformation: ____ second transformation: ____ vertical translation horizontal translation reflection over vertical line m reflection over horizontal line k 90° clockwise rotation about point p 180° clockwise rotation about point p

Explanation:

Step1: Analyze Rotation

First, a \(180^\circ\) clockwise rotation about point \(p\) can align the orientation of Figure 1 towards Figure 2. A \(180^\circ\) rotation swaps the direction, which matches the orientation change here.

Step2: Analyze Translation

After rotation, a vertical translation (moving up/down) or horizontal translation (moving left/right) can position it. But looking at the grid, after \(180^\circ\) rotation about \(p\), a vertical translation (or checking the other option: reflection? No, rotation first. Wait, another approach: First, \(180^\circ\) clockwise rotation about \(p\) (changes orientation), then vertical translation? Wait, no, let's check the options. The rotation options: \(180^\circ\) clockwise about \(p\) is a key. Then, vertical translation? Wait, the other transformations: reflection over vertical line \(m\), horizontal translation, etc. Wait, the correct sequence: First, \(180^\circ\) clockwise rotation about point \(p\) (changes the figure's orientation to match Figure 2's orientation), then vertical translation (to move it to the position of Figure 2). Wait, no, let's see the figure. Figure 1 and Figure 2: after rotating \(180^\circ\) about \(p\), the figure's direction is reversed, then a vertical translation (or horizontal? Wait, the options for translation: vertical or horizontal. Wait, the first transformation: \(180^\circ\) clockwise rotation about point \(p\), second transformation: vertical translation. Wait, no, maybe first \(180^\circ\) rotation, then vertical translation. Alternatively, first reflection? No, rotation is better. Let's confirm: A \(180^\circ\) rotation about \(p\) will flip the figure both horizontally and vertically, then a vertical translation (or horizontal) to match. But the options for translation: vertical or horizontal. Let's check the positions. After \(180^\circ\) rotation about \(p\), the figure is oriented like Figure 2, then a vertical translation (moving up/down) or horizontal? Wait, the correct first transformation is \(180^\circ\) clockwise rotation about point \(p\), second is vertical translation. Wait, no, maybe the first is \(180^\circ\) rotation, second is vertical translation. Let's proceed.

Step1: First Transformation

The first transformation is \(180^\circ\) clockwise rotation about point \(p\). This is because rotating Figure 1 \(180^\circ\) around \(p\) will align its orientation with Figure 2 (since \(180^\circ\) rotation reverses the direction, matching the arrow's direction in Figure 2).

Step2: Second Transformation

After the \(180^\circ\) rotation, a vertical translation (moving the figure vertically) will position it exactly at Figure 2's location. Alternatively, horizontal? Wait, no, the vertical translation option is there. Wait, the translation options: vertical or horizontal. After rotation, the vertical translation (moving up/down) will adjust the position. So first transformation: \(180^\circ\) clockwise rotation about point \(p\), second transformation: vertical translation.

Answer:

First transformation: \(180^\circ\) clockwise rotation about point \(p\)
Second transformation: Vertical translation