Question
Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)
Responses
Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.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 x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Image with alt text: Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Image with alt text: Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Responses
Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.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 x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Image with alt text: Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Image with alt text: Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Answers
Answered by
GPT-4o mini
The transformation that preserves both distance and angle measure is known as a rigid transformation or an isometry. Among the graphs you've described, the one that represents two equivalent triangles is the most likely to demonstrate a rigid transformation. This is because equivalent triangles maintain their size and shape, ensuring that distances and angles are preserved during their movement from one quadrant to another.
So, the correct response would be:
**Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.**
So, the correct response would be:
**Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.**