Which transformation changes triangle ABC to triangle A’B’C’?

Mathematics · Middle School · Thu Feb 04 2021

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1. Translation: This moves every point of a shape the same distance in the same direction. In the case of a triangle, if triangle A'B'C' is found by sliding triangle ABC along a straight path without rotating or flipping it, then the transformation is a translation.

2. Rotation: This turns a shape around a fixed point called the center of rotation. If triangle A'B'C' can be obtained by rotating triangle ABC around a point (not necessarily one of the vertices) by a certain angle in a particular direction (clockwise or counterclockwise), then the transformation is a rotation.

3. Reflection: This is a mirror image of a shape across a line called the line of reflection. If triangle A'B'C' looks like the mirror image of triangle ABC across a certain line, then the transformation is a reflection.

4. Dilation: This involves enlarging or reducing a shape proportionally in size. If triangle A'B'C' is a scaled-up or scaled-down version of triangle ABC, while maintaining the same center of dilation (which can be a point on the triangle, inside it, or outside it), then the transformation is a dilation.

Without specific information or visual representation of the triangles ABC and A'B'C', we cannot definitively say which transformation was applied. However, by comparing the corresponding sides and angles of both triangles, one could determine whether they are congruent (same shape and size), similar (same shape but different size), or neither, which could give insight into which of the aforementioned transformations has been applied.