Question

quadrilateral army is rotated 90° about the origin. draw the image of this rotation.

Explanation:

Step1: Identify Coordinates

First, find the coordinates of each vertex of quadrilateral ARMY:

• \( A(3, 3) \)
• \( R(5, 7) \)
• \( M(7, 5) \)
• \( Y(5, 1) \)

Step2: Apply 90° Rotation Rule

The rule for a 90° counterclockwise rotation about the origin is \( (x, y) \to (-y, x) \). For clockwise, it's \( (x, y) \to (y, -x) \). Assuming counterclockwise (standard unless stated):

• \( A(3, 3) \to (-3, 3) \)
• \( R(5, 7) \to (-7, 5) \)
• \( M(7, 5) \to (-5, 7) \)
• \( Y(5, 1) \to (-1, 5) \)

Step3: Plot Rotated Points

Plot the new points \( A'(-3, 3) \), \( R'(-7, 5) \), \( M'(-5, 7) \), \( Y'(-1, 5) \) and connect them to form the rotated quadrilateral.

Answer:

The rotated quadrilateral has vertices at \( (-3, 3) \), \( (-7, 5) \), \( (-5, 7) \), \( (-1, 5) \) (plotted and connected on the grid).