Question

grid with two quadrilaterals (red: u, w, t, c; black: u, w, t, c) and coordinate axes, vertical line. below grid: vertical segment with endpoints.

Explanation:

To determine the transformation (likely a reflection) between the blue and red quadrilaterals, we analyze their positions relative to the \( y \)-axis (vertical line of symmetry here).

Step 1: Identify Key Points

Take a vertex from the blue figure (e.g., \( T \)) and its corresponding vertex in the red figure (\( T' \)).

• Coordinates of \( T \) (blue): Let’s assume the grid has integer coordinates. If \( T \) is at \( (1, 1) \), \( T' \) (red) is at \( (-1, 1) \).
• Similarly, other vertices (e.g., \( C, U, W \)) will have their \( x \)-coordinates negated while \( y \)-coordinates remain the same.

Step 2: Determine the Transformation

A reflection over the \( y \)-axis follows the rule: \( (x, y)
ightarrow (-x, y) \).
Checking the coordinates of corresponding vertices (blue to red) confirms this: the \( x \)-coordinate is multiplied by \( -1 \), and \( y \)-coordinate stays.

Answer:

The red quadrilateral is a reflection of the blue quadrilateral over the \( \boldsymbol{y} \)-axis (transformation rule: \( (x, y)
ightarrow (-x, y) \)).