Question

two similar triangles are shown.
△mno was dilated, then _, to create
△yhq.
rotated
reflected
translated
dilated

Explanation:

• Rotation: Rotation changes the orientation of a figure around a fixed point. But looking at the triangles, the orientation change is not just a rotation.
• Reflection: Reflection flips a figure over a line. If we assume a vertical or horizontal line of reflection, the position of the angles (the marked angles in \(\triangle MNO\) and \(\triangle YHQ\)) does not match a simple reflection.
• Translation: Translation slides a figure without rotation or reflection. The orientation and relative position of the angles (the non - congruent position of the marked angles in the two triangles) rules out translation.
• Dilation: Dilation changes the size of a figure. But the problem states that \(\triangle MNO\) was already dilated. After dilation, if we consider the orientation of the triangles (the order of the vertices and the position of the angles), we can observe that if we reflect \(\triangle MNO\) (over a suitable line, for example, if we assume a reflection over a line that changes the order of the vertices' arrangement while keeping the angle measure and side - ratio (due to similarity) consistent), we can get \(\triangle YHQ\).

Answer:

reflected