Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?
Figure A, Figure B, Figure C, Figure D

Solution:

When a point is reflected across the line y = x the x and y coordinates change its place.

It provides such a reflection rule

(x, y) → (y, x)

Using the figure

L (3, 1), M (4, 3), N (5, 3) and P (4, 1)

From the reflection rule, the coordinates of image points can be found

L’ (1, 3), M’ (3, 4), N’ (3, 5) and P’ (1, 4)

These are the coordinates of vertices of the figure C.

Therefore, figure C represents the image of parallelogram LMNP.

Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?
Figure A, Figure B, Figure C, Figure D

Summary:

The figure which represents the image of parallelogram LMNP after a reflection across the line y=x is Figure C.