Question

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

Explanation:

To determine the correct reflection of \( \triangle ABC \) across line \( \ell \), we use the property of reflections: the line of reflection (\( \ell \)) is the perpendicular bisector of the segment joining a point and its image.

Step 1: Analyze Point Reflections

For a reflection across line \( \ell \), each vertex of \( \triangle ABC \) (e.g., \( A, B, C \)) must have its image \( A', B', C' \) such that \( \ell \) is the perpendicular bisector of \( AA' \), \( BB' \), and \( CC' \).

Step 2: Evaluate the Options

• First Option (Top Choice): Check if \( A' \), \( B' \), \( C' \) are correctly reflected. The segments from \( A \) to \( A' \), \( B \) to \( B' \), and \( C \) to \( C' \) are bisected by \( \ell \), and \( \ell \) is perpendicular to these segments (visually, the grid confirms equal distance from \( \ell \) for each point and its image).
• Other options fail: For example, the second option misplaces \( C' \) (not equidistant from \( \ell \) as \( C \)), the third option misaligns \( B' \), and the fourth option shifts the triangle incorrectly.

Answer:

The first (top) option (with the red and blue points) is the correct reflection of \( \triangle ABC \) across line \( \ell \).