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Problem 181

Geometry Difficulty 1.4 Multiple choice CEMC Gauss (Grade 7) · Canada · 2017

When the shaded triangle shown is translated, which of the following triangles can be obtained?


Hide/Reveal Description of Triangles

Shaded triangle: Starting at the vertex of the 90 degree angle, one side measures 4 units up and the other side measures 6 units right. The hypotenuse then completes the triangle.
Triangle A: Starting at the vertex of the 90 degree angle, one side measures 4 units down and the other side measures 6 units right.
Triangle B: Starting from the vertex of the 90 degree angle, one side measures 4 units right and the other side measures 6 units up.
Triangle C: Starting from the vertex of the 90 degree angle, one side measures 4 units up and the other side measures 6 units left.
Triangle D: Starting from the vertex of the 90 degree angle, one side measures 4 units up and the other side measures 6 units right.
Triangle E: Starting from the vertex of the 90 degree angle, one side measures 4 units right and the other side measures 6 units up.

Pick one

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Official solution

A translation moves (slides) an object some distance without altering it in any other way.

That is, the object is not rotated, reflected, and its exact size and shape are maintained.

Of the triangles given, the triangle labelled DD is the only triangle whose orientation is identical to that of the shaded triangle.

Thus, DD is the triangle which can be obtained when the shaded triangle is translated.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.