To demonstrate that two figures (Figure 1 and Figure 2) are similar, one typically shows that a series of transformations—such as reflections, translations, rotations, and dilations—can be applied to one figure to obtain the other.
Here's a breakdown of the transformations described in the four response options:
Option A:
- Reflects Figure 1 across the y-axis.
- Translates the reflected figure down 1 unit and left 2 units.
- Dilates the result by a scale factor of 1/2.
Option B:
- Reflects Figure 1 across the y-axis.
- Translates the reflected figure down 3 units and left 2 units.
- Dilates by a scale factor of 1/2.
Option C:
- Rotates Figure 1 clockwise from the origin by 90°.
- Translates the rotated figure down 3 units and left 2 units.
- Dilates by a scale factor of 1/2.
Option D:
- Rotates Figure 1 clockwise from the origin by 180°.
- Reflects the figure across the x-axis.
- Translates the result down 1 unit and left 3 units.
- Dilates by a scale factor of 1/2.
To determine which response correctly describes the transformations required to show that Figure 1 is similar to Figure 2, you would need to analyze the specific characteristics and orientation of both figures.
In general, similar figures can be obtained through a combination of the types of transformations listed above. A routine way to confirm similarity includes checking:
- Proportionality of corresponding sides (after dilation)
- Preservation of angle measures (through rotations and reflections)
If you have additional information about Figure 1 and Figure 2 (e.g., coordinates, side lengths), you could narrow down to the correct transformation pathway. If no such information is provided, you might have to rely on visual inspection or geometric reasoning to select the most fitting transformation sequence.
For a final answer, you would select the option that accurately describes the steps taken from Figure 1 to Figure 2.
1 answer