Question

An architect planned to put a fountain in a customer's courtyard. He plotted the shape of the fountain on the coordinate grid below. The customer wants the fountain to be moved so that the vertices are at points on the coordinate grid. Which transformations will move the original fountain region onto the new fountain region? Select ALL that apply.

A) Reflect across the x-axis, then translate 5 units right and 4 units up.
B) Reflect across the y-axis, then translate 4 units left and 3 units down.
C) Reflect across the line y=x, then translate 2 units right and 7 units down.
D) Rotate 90 degrees counterclockwise about the origin, then translate 2 units right and 7 units up.

Answer 1

To transform the fountain shape to its new location, Option A and D are possible transformations that move the fountain right and up, with A reflecting across the x-axis, and D involving a 90 degrees rotation before translating.

Step-by-step explanation:

The student's question pertains to identifying which transformations will move the original fountain region onto the new fountain region on a coordinate grid. The transformations include reflections, translations, and rotations.

Option A involves reflecting across the x-axis, then translating 5 units right and 4 units up. This moves the fountain horizontally to the right side of the coordinate system and vertically upward.

Option B incorporates reflecting across the y-axis, then translating 4 units to the left and 3 units down, covering horizontally to the left side and vertically downward movements.

Option C entails a reflection across the line y=x, followed by a translation of 2 units to the right and 7 units down, indicating a horizontal rightward and vertical downward shift.

Option D involves a 90 degrees counterclockwise rotation about the origin, followed by a translation 2 units to the right and 7 units up.