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Geometry Practice Problems: Reflections and Rotations

Practice problems on reflecting points across axes, translating coordinates, and rotating shapes to reinforce geometric concepts. Learn methods, rules, and examples for better understanding.

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Geometry Practice Problems: Reflections and Rotations

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  1. Warm Up 1. A point P has coordinates (1, 4). What are its new coordinates after reflecting point P across the x-axis? [A] (-1, 4) [B] (1, 4) [C] (1, -4) [D] (-1, -4) 2. Identify the coordinates of the image point formed by reflecting (3, -6) across the y-axis.   [A] (3, 6) [B] (-3, -6) [C] (3, -6) [D] (-3, 6) 3. Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of the first star are at (4, 1). The star is translated left 5 units. What are its new coordinates? [A] (-1, 1) [B] (4, 6) [C] (9, 1) [D] (4, -4) 6. Write the translation of point P(2, -9) to point P’(-1,-11).    [A] (x,y) to (x -3, y-2) [B]  (x, y) to (x + 3, y +2) [C] (x, y) to (x + 2, y +3) [D]  (x, y) to (x – 2, y – 3)

  2. Rotations The figure turns around a fixed point.

  3. Rotation" means turning around a center: The distance from the center to any point on the shape stays the same. • Every point makes a circle around the center.

  4. Rotate 90° • Rule (x,y) flips to (y,x) *See what quadrant you end up in for the signs. EX: (1,2) rotated clock wise ends up in quadrant IV (1,-2)

  5. Rotate 180° • Rule (x,y) does not flip but signs change (-x,-y) EX: (-5,-1) becomes (5,1)

  6. Rotate 270° • Rule (x,y) flips to (y,x). *See what quadrant you end up in for the signs. EX: (5,6) rotated in a clockwise direction ends up in quadrent II so, (-6,5)

  7. a) Rotate Triangle ABC 90 counterclockwise. b) Rotate Triangle ABC 180 counterclockwise.C) Rotate Triangle ABC 270 counterclockwise.

  8. Rotate 360° • What would happen to the figure if you rotated it 360°? • Video

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