Question
Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)
Responses
The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Image with alt text: The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Two triangles are plotted on a coordinate plane. One of them is in quadrant 1 and the other starts in quadrant 2 and crosses into quadrant 1.
Image with alt text: Two triangles are plotted on a coordinate plane. One of them is in quadrant 1 and the other starts in quadrant 2 and crosses into quadrant 1.
The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Image with alt text: The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Two triangles of different sizes are plotted on a coordinate plane. The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Image with alt text: Two triangles of different sizes are plotted on a coordinate plane. The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Responses
The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Image with alt text: The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Two triangles are plotted on a coordinate plane. One of them is in quadrant 1 and the other starts in quadrant 2 and crosses into quadrant 1.
Image with alt text: Two triangles are plotted on a coordinate plane. One of them is in quadrant 1 and the other starts in quadrant 2 and crosses into quadrant 1.
The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Image with alt text: The graph on the coordinate plane shows two squares, a smaller one inside a larger one, plotted in quadrant 1.
Two triangles of different sizes are plotted on a coordinate plane. The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Image with alt text: Two triangles of different sizes are plotted on a coordinate plane. The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Answers
Answered by
GPT-4o mini
The transformation that preserves both distance and angle measure is called an **isometry**. Among the graphs described, the one demonstrating an isometric transformation is likely the one showing two squares, since squares are congruent shapes and this implies that distances and angles are preserved through the transformation.
In your options, you mentioned:
1. Two squares, one inside the other.
2. Two triangles that cross quadrants.
3. Two triangles of different sizes.
Since the squares are similar and congruent, the graph showing the two squares (the first and the third description you provided are identical) indicates a transformation (such as translation, rotation, or reflection) that preserves distances and angles. Thus, they demonstrate the preservation characteristics of an isometry.
Therefore, the answer is the graph that shows **two squares, a smaller one inside a larger one**.
In your options, you mentioned:
1. Two squares, one inside the other.
2. Two triangles that cross quadrants.
3. Two triangles of different sizes.
Since the squares are similar and congruent, the graph showing the two squares (the first and the third description you provided are identical) indicates a transformation (such as translation, rotation, or reflection) that preserves distances and angles. Thus, they demonstrate the preservation characteristics of an isometry.
Therefore, the answer is the graph that shows **two squares, a smaller one inside a larger one**.