Question

question 18
1 pts
in the diagram, △abc is the image of △abc. which type of transformation is shown?
options: reflection, translation, dilation, rotation
question 19
1 pts
in the diagram, △xyz is the image of △xyz. which type of transformation is shown?

Explanation:

Question 18

To determine the transformation, we analyze the positions of \( \triangle ABC \) and \( \triangle A'B'C' \). A reflection over the \( y \)-axis (vertical line) would map a point \( (x,y) \) to \( (-x,y) \). Observing the coordinates (from the grid), points like \( A \) and \( A' \), \( B \) and \( B' \), \( C \) and \( C' \) are symmetric with respect to the \( y \)-axis. Translation would move the figure without flipping, dilation changes size, and rotation involves turning (not symmetric over an axis here). So the transformation is reflection.

For \( \triangle XYZ \) and \( \triangle X'Y'Z' \), a translation is a transformation that slides a figure from one position to another without changing its shape, size, or orientation. If the triangles are moved (e.g., horizontally) without flipping (reflection), resizing (dilation), or turning (rotation), then it's a translation.

Answer:

A. reflection

Question 19 (assuming the diagram shows a translation, as the triangles \( \triangle XYZ \) and \( \triangle X'Y'Z' \) seem to be moved without flipping, resizing, or rotating, just shifting horizontally/vertically)