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 rule for reflection across \(y = x\)

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

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

Parallelogram \(LMNP\) is in the first - quadrant. When we reflect a figure in the first - quadrant across \(y = x\), the \(x\) and \(y\) coordinates of its vertices are swapped.

Step3: Analyze each figure

• Figure \(A\) is in the third - quadrant. A reflection of a first - quadrant figure across \(y=x\) will not be in the third - quadrant.
• Figure \(B\) is in the second - quadrant. A reflection of a first - quadrant figure across \(y=x\) will not be in the second - quadrant.
• Figure \(C\): If we consider the general orientation and the fact that reflecting a figure in the first - quadrant across \(y = x\) swaps the \(x\) and \(y\) “distances” from the axes. A figure in the first - quadrant, when reflected across \(y=x\), will still be in a “quadrant - like” position (in terms of relative position to the axes) that matches figure \(C\).
• Figure \(D\) is in the fourth - quadrant. A reflection of a first - quadrant figure across \(y=x\) will not be in the fourth - quadrant.

Answer:

figure C