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 the reflection rule

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

Step2: Analyze the position of parallelogram \(LMNP\)

Parallelogram \(LMNP\) is in the first - quadrant. After reflection across \(y=x\), the image should be in the region where the \(x\) and \(y\) coordinates of its vertices are swapped. Figure \(C\) is in the second - quadrant (if we consider the general orientation of the coordinate system in the given grid). But actually, if we consider the transformation of each point of parallelogram \(LMNP\) (in the first - quadrant near \(x = 3,4\) and \(y=1,2\)), after reflection \(y=x\), the \(x\) and \(y\) values of its vertices will be swapped. Looking at the positions of the figures: figure \(C\) has the correct orientation and position based on the reflection rule \( (x,y)\to(y,x)\) for each of its vertices.

Answer:

figure C