Question

1. quadrilateral prst is transformed according to the rule (x, y) → (x + 9, y + 4) to create quadrilateral prst.

graph of coordinate plane with quadrilateral prst
which statement is true?

• the side lengths of quadrilateral prst are twice the corresponding side lengths of quadrilateral prst.
• the angle measures of quadrilateral prst are equal to the corresponding angle measures of quadrilateral prst.
• the side lengths of quadrilateral prst are 9 units longer than the corresponding side lengths of quadrilateral prst.
• the angle measures of quadrilateral prst are greater than the corresponding angle measures of quadrilateral prst.

Explanation:

The transformation rule \((x,y)\to(x + 9,y + 4)\) is a translation (a type of rigid transformation). Rigid transformations preserve the shape and size of the figure, meaning side lengths and angle measures remain unchanged.

• The first option is wrong because translation doesn't scale side lengths (twice the length would be a dilation, not translation).
• The third option is wrong because translation moves the figure, it doesn't add a fixed length to each side.
• The fourth option is wrong because rigid transformations preserve angle measures, so angles don't increase.
• The second option is correct as translation (rigid transformation) preserves angle measures.

Answer:

The angle measures of quadrilateral \(P'R'S'T'\) are equal to the corresponding angle measures of quadrilateral \(PRST\).