Question

plot the image of triangle △abc under a reflection across line ℓ.

Explanation:

Step1: Find reflection of A

Draw a perpendicular from A to line \( \ell \), measure the distance from A to \( \ell \), mark a point \( A' \) on the other side of \( \ell \) at the same distance.

Step2: Find reflection of B

Draw a perpendicular from B to line \( \ell \), measure the distance from B to \( \ell \), mark a point \( B' \) on the other side of \( \ell \) at the same distance.

Step3: Find reflection of C

Draw a perpendicular from C to line \( \ell \), measure the distance from C to \( \ell \), mark a point \( C' \) on the other side of \( \ell \) at the same distance.

Step4: Connect \( A', B', C' \)

Join the reflected points \( A', B', C' \) to form the reflected triangle \( \triangle A'B'C' \).

(Note: Since this is a plotting task, the actual plotting would involve using the grid to accurately determine the perpendicular distances and mark the reflected points. The key is that each vertex's reflection is equidistant from line \( \ell \) as the original vertex, on the opposite side.)

Answer:

The image of \( \triangle ABC \) under reflection across line \( \ell \) is \( \triangle A'B'C' \) where \( A', B', C' \) are the reflections of \( A, B, C \) across \( \ell \) (plotted by ensuring each is equidistant from \( \ell \) on the opposite side and connecting them).