Question

the graph shows pentagons pqrst and pqrst. which of the following transformations maps pqrst onto pqrst?

Explanation:

To determine the transformation mapping \( PQRST \) onto \( P'Q'R'S'T' \), we analyze the coordinates of corresponding vertices (e.g., \( P(10, 8) \) to \( P'(-3, 5) \), \( Q(10, 1) \) to \( Q'(-3, -1) \), etc.).

Step 1: Analyze Horizontal (x - axis) Shift

For a point \( (x, y) \) in \( PQRST \), the x - coordinate of its image in \( P'Q'R'S'T' \) is \( x - 13 \) (e.g., \( 10-13=-3 \) for \( P \) to \( P' \)).

Step 2: Analyze Vertical (y - axis) Shift

The y - coordinate of the image is \( y - 3 \) (e.g., \( 8 - 3=5 \) for \( P \) to \( P' \)).

Step 3: Check for Reflection (Optional, but here shift is primary)

Since the shape’s orientation (e.g., angles, side - length ratios) is preserved, and we have a consistent horizontal shift of \( - 13 \) (left 13 units) and vertical shift of \( - 3 \) (down 3 units), the transformation is a translation (specifically, \( (x,y)\to(x - 13,y - 3) \)).

Answer:

A translation 13 units to the left and 3 units down (or equivalent vector - based description of the shift).