Question

two similar triangles are shown.
△xyz was dilated, then _________, to create △qag.
options: translated, dilated, reflected, rotated

Explanation:

Step1: Analyze Dilation Effect

Dilation changes size, here triangles are similar (so dilation done). Now check orientation change.

Step2: Check Transformations

• Translate: moves without flip/rotate, but orientation here flipped? No, wait, reflection over the vertical line (the purple line) would flip the triangle. Wait, the original triangle XYZ and QAG: after dilation (making smaller), the reflection over the vertical line (the purple axis) would map XYZ to QAG? Wait, no, the options: translated (move), dilated (already done), reflected (flip over line), rotated (turn). Looking at the triangles, after dilation (making QAG smaller than XYZ), the triangle QAG is a mirror image over the vertical line (the purple line) of the dilated XYZ? Wait, no, the vertical line is between them. So after dilation, reflecting over that vertical line would create QAG. Wait, but the options: the third option is "reflected". Wait, let's see the angle: in XYZ, angle at Y; in QAG, angle at A. The orientation: if we reflect over the vertical line, the triangle would flip. So after dilation (to make size same as QAG), then reflected over the vertical line. So the correct transformation after dilation is reflection. Wait, but let's check the options again. The options are translated, dilated, reflected, rotated. Since dilation is already done (the first transformation), the next is reflection. Wait, maybe I misread. Wait, the problem says "△XYZ was dilated, then ______ to create △QAG". So after dilation (changing size), what's next? Let's look at the position and orientation. The triangle QAG is on the other side of the vertical line, mirror image. So reflection. So the correct option is "reflected". Wait, but let's confirm: translation is moving, rotation is turning, reflection is flipping over a line, dilation is resizing. Since after dilation (resizing), the triangle is flipped over the vertical line (the purple line) to get QAG. So the answer is reflected.

Answer:

reflected (the third option, labeled as "reflected")