Question

which figure represents the image of parallelogram lmnp after a reflection across the line ( y = x )? figure a figure b figure c figure d

Explanation:

Step1: Recall reflection rule

When reflecting a point \((x,y)\) across the line \(y = x\), the transformation rule is \((x,y)\to(y,x)\).

Step2: Analyze the position of parallelogram LMNP

Assume the coordinates of the vertices of parallelogram LMNP. After reflection across \(y = x\), the \(x\) and \(y\) - coordinates of each vertex are swapped.

Step3: Compare with figures

By visual inspection (since we can't calculate exact coordinates without them, but using the general property of reflection over \(y=x\) which swaps the \(x\) and \(y\) positions of points in the plane), figure \(C\) has the correct orientation and position relative to the line \(y = x\) as a reflection of parallelogram LMNP.

Answer:

figure C