Question

the figure on the left is reflected using line ℓ to form the image on the right. which of the following shows the corresponding parts in the image labeled correctly? a) description of option a with angles and side - lengths b) description of option b with angles and side - lengths c) description of option c with angles and side - lengths d) description of option d with angles and side - lengths

Explanation:

Step1: Recall reflection properties

In a reflection, corresponding side - lengths are equal and corresponding angles are equal. Also, the orientation of the figure changes (left - right is reversed).

Step2: Analyze side - lengths

The side - lengths of the original figure are 2.2 and 3.2. In a reflection, these side - lengths should be the same in the image. All options seem to have the correct side - lengths.

Step3: Analyze angle positions

When a figure is reflected over a vertical line, the left - right position of the angles changes. The original figure has angles 143°, 63°, and 108° in a certain left - right order. In the reflected figure, the order of these angles from left to right should be reversed.
For the original figure, if we consider the angles from left - most to right - most, in the reflected figure, the left - most angle of the original should be the right - most angle of the reflected figure and vice - versa.
Option A has the angles in the same left - right order as the original figure, which is incorrect for a reflection.
Option C has incorrect angle - side correspondences.
Option D has incorrect angle positions.
Option B has the correct reversal of the left - right order of the angles while maintaining the correct side - lengths and angle measures.

Answer:

B.