Question

triangle jkl is reflected across x = 0 and then translated 5 units up to create △jkl. are the two figures congruent? explain.
a. no; a reflection changes the orientation of a figure, so the figures are not congruent.
b. no; a translation changes the position of a figure, so the figures are not congruent.
c. yes; reflections and translations preserve lengths and angle measures, so the figures are congruent.
d. there is not enough information.

Explanation:

To determine if the triangles are congruent, we analyze the transformations: reflection (over \(x = 0\)) and translation (5 units up). Both reflection and translation are rigid transformations. Rigid transformations (reflections, translations, rotations) preserve the lengths of sides and the measures of angles of a figure, meaning the pre - image and the image after a rigid transformation are congruent.

• Option A is incorrect because a reflection is a rigid transformation that preserves congruence (orientation change does not affect congruence).
• Option B is incorrect because translation is a rigid transformation that preserves congruence (changing position does not affect congruence).
• Option D is incorrect because we have enough information about the transformations (reflection and translation, both rigid) to determine congruence.
• Option C is correct as reflections and translations are rigid transformations that preserve lengths and angle measures, so the figures are congruent.

Answer:

C. Yes; reflections and translations preserve lengths and angle measures, so the figures are congruent.