Question

5 the points given below are the vertices of △vwx and its image after a reflection. v(2, 1), w(3, 5), x(4, 2) v(-2, 1), w(-3, 5), x(-4, 2) a. what do you notice when you compare corresponding x-coordinates and corresponding y-coordinates of the vertices of △vwx and △vwx?

Explanation:

To answer this, we compare the coordinates of the original triangle \( \triangle VWX \) and its image \( \triangle V'W'X' \).

For the \( x \)-coordinates:

• \( V \) has \( x = 2 \), \( V' \) has \( x = -2 \) (opposite sign)
• \( W \) has \( x = 3 \), \( W' \) has \( x = -3 \) (opposite sign)
• \( X \) has \( x = 4 \), \( X' \) has \( x = -4 \) (opposite sign)

For the \( y \)-coordinates:

• \( V \) has \( y = 1 \), \( V' \) has \( y = 1 \) (same)
• \( W \) has \( y = 5 \), \( W' \) has \( y = 5 \) (same)
• \( X \) has \( y = 2 \), \( X' \) has \( y = 2 \) (same)

So, the \( y \)-coordinates of corresponding vertices are equal, and the \( x \)-coordinates are opposites (i.e., \( (x,y) \to (-x,y) \), which is a reflection over the \( y \)-axis).

Answer:

When comparing corresponding vertices, the \( y \)-coordinates are the same, and the \( x \)-coordinates are opposites (e.g., \( V(2,1) \) and \( V'(-2,1) \), \( W(3,5) \) and \( W'(-3,5) \), \( X(4,2) \) and \( X'(-4,2) \)). This indicates a reflection over the \( y \)-axis, where the transformation rule is \( (x,y) \to (-x,y) \).