Question

select the parallelogram that represents the reflection of parallelogram x across the y-axis.

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\). So we need to check the coordinates of the vertices of parallelogram \(X\) and see which parallelogram (A, B, or C) has vertices that are the reflection of \(X\)'s vertices over the \(y\) - axis.

Step2: Analyze coordinates (visually)

Let's assume the vertices of parallelogram \(X\) are in the first and fourth quadrants (since it's red and on the right side of the \(y\) - axis). When we reflect over the \(y\) - axis, the \(x\) - coordinates will be negated and \(y\) - coordinates remain the same. Parallelogram \(C\) is on the left side of the \(y\) - axis, and if we take a vertex of \(X\) with coordinates \((x,y)\), the corresponding vertex of \(C\) should be \((-x,y)\). By visually inspecting the grid, the shape and position of parallelogram \(C\) is the reflection of \(X\) over the \(y\) - axis (since reflection over \(y\) - axis flips the figure horizontally across the \(y\) - axis, and \(C\) is the mirror image of \(X\) with respect to the \(y\) - axis). Parallelogram \(A\) is a reflection over the \(x\) - axis (since it's above \(X\) and \(y\) - coordinates are negated) and parallelogram \(B\) is not a reflection over \(y\) - axis (its position is not the mirror image of \(X\) over \(y\) - axis).

Answer:

Parallelogram C