Question

question 3 draw the image of △abc after a reflection across line ℓ.

Explanation:

To determine the correct reflection of \(\triangle ABC\) across line \(\ell\) (the diagonal line, likely \(y = x\) or a line with slope \(1\)):

Key Property of Reflection:

For a reflection across a line (here, the diagonal), the distance from each vertex of the original triangle to the line \(\ell\) must equal the distance from the reflected vertex to \(\ell\). Also, the line \(\ell\) is the perpendicular bisector of the segment joining a vertex and its image.

Analyzing the Options:

• First (blue - marked) Option: Check the distances and symmetry. For each vertex \(A, B, C\), their reflections \(A', B', C'\) should be equidistant from \(\ell\) and form a mirror image. This option correctly reflects each point across \(\ell\) (e.g., vertical/horizontal distances to \(\ell\) are preserved in the reflected points).
• Other options fail:
• The second (red - marked) option misplaces \(C'\) (distance to \(\ell\) is not preserved).
• The third option misreflects \(A\) and \(B\) (symmetry is broken).
• The fourth option distorts the triangle’s shape relative to \(\ell\).

Answer:

The first (blue - selected) option (the one with the red triangle \(A'B'C'\) where \(A'\), \(B'\), \(C'\) are symmetric to \(A\), \(B\), \(C\) across line \(\ell\)).