Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)

Question

Responses which is the only true correct answer that is 100 percent correcr and why by giving me explanation

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 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.
Image with alt text: 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.

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.

Answer 1

The transformation that preserves both distance and angle measure is called a rigid transformation, which includes translations, rotations, and reflections.

In this case, the graph that demonstrates a transformation that preserves both distance and angle measure is the second option:

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.

Explanation:

• Equivalent Triangles: The two triangles are described as equivalent, meaning they have the same shape and size. The property of equivalence implies that their sides are of equal length and their angles are of equal measure.
• Positioning: One triangle is in quadrant 1, while the second triangle starts in quadrant 2 and crosses into quadrant 1. This indicates a possible rigid transformation (like rotation or reflection) that does not alter distances between points or the angles between lines.
• Linear Connection: The mention of a line connecting matching vertices suggests that the transformation between these two triangles involves maintaining the congruency, supporting that the shape and sizes are unchanged, which is characteristic of rigid transformations.

In contrast:

1. The first option shows two squares but involves one square situated inside another, which indicates scaling (not preserving distance).
2. The third option involves two triangles of different sizes, meaning it’s a dilation transformation which does not preserve distance and angle measures between the shapes.

Thus, the second option with the equivalent triangles is the only graph that maintains both distance and angle measure, confirming it as the correct answer.