Question

question
determine the line of reflection that would map the pink figure onto the dotted outline of the image under the reflection.
click and drag the yellow dots to change the line. click and drag the line itself to move it in parallel.

Explanation:

Step1: Recall Reflection Properties

A reflection over the line \( y = x \) swaps the \( x \)- and \( y \)-coordinates of a point \((x, y)\) to \((y, x)\). We check the symmetry of the pink triangle and its image (dotted and light blue) with respect to this line.

Step2: Analyze Coordinate Symmetry

For a reflection over \( y = x \), each vertex of the pink figure should have its image with swapped coordinates. Observing the graph, the line \( y = x \) (passing through the origin with a slope of 1) aligns the pink triangle and its reflected image, as the symmetry across \( y = x \) matches the positions of the vertices.

Answer:

The line of reflection is \( y = x \) (the line with slope 1 passing through the origin).