Rigid transformations and congruence

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. Translate the point A(−4,−4)A(-4, -4) by 2 units right and 1 units down. Tap its image A′A'.
  2. A translation takes (−3,0)(-3, 0) to (0,5)(0, 5). By how many units does it move points horizontally (positive = right)?
  3. A polygon with 9 sides is translated. What changes?
    1. Only its position: lengths and angles stay the same
    2. Its side lengths
    3. Its angles
  4. Translate triangle ABC 2 right and 2 down. Tap the images A′, B′ and C′.
  5. Reflect A(3,2)A(3, 2) across the xx-axis. Tap its image.
  6. Reflect A(5,−1)A(5, -1) across the line y=xy = x. Tap its image.
  7. A point is 5 units from a line of reflection. How far is it from its image?
  8. Reflect triangle ABC across the yy-axis. Tap the images A′, B′ and C′.
  9. Rotate A(1,3)A(1, 3) by 90∘90^\circ counterclockwise about the origin. Tap its image.
  10. Rotate A(−2,−1)A(-2, -1) by 180∘180^\circ about the origin. Tap its image.
  11. A figure is rotated 7 times by 90∘90^\circ in the same direction. What single rotation, between 0∘0^\circ and 360∘360^\circ, gives the same result? (degrees)
  12. Rotate triangle ABC by 90° counterclockwise about the origin. Tap the images A′, B′ and C′.