Geometric Transformations Quiz

Grade 8 · Math · Quiz

Apply transformation rules on the coordinate plane.

Questions

Point (4, -3) translated by (x-2, y+5). New coordinates?
1. (2, 2)
2. (6, -8)
3. (2, -8)
4. (6, 2)
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Answer: (2, 2)
x: 4-2=2; y: -3+5=2.
A rotation is a rigid motion that preserves size and shape.
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Answer: True
Rotations preserve distances and angles — they are isometries.
Reflecting (5, 3) over the y-axis gives (___, 3).
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Answer: -5
Reflection over y-axis: (x,y) becomes (-x,y). So (5,3) becomes (-5,3).
Dilation with scale factor 0.5. The image is:
1. Twice as large
2. Same size
3. Half as large
4. Rotated 90 degrees
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Answer: Half as large
Scale factor 0.5 multiplies every coordinate by 0.5, halving all lengths.
Point (3, 4) rotated 90 degrees CCW about origin. New point?
1. (-4, 3)
2. (4, -3)
3. (-3, -4)
4. (4, 3)
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Answer: (-4, 3)
90 degree CCW: (x,y) becomes (-y,x). So (3,4) becomes (-4,3).
A translation changes the orientation (direction) of a figure.
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Answer: False
Translation slides every point equally without changing orientation.
A dilation that enlarges has a scale factor ___ than 1.
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Answer: greater
Scale factor k>1 enlarges the figure.
Which transformation maps (2, 3) to (-2, -3)?
1. Reflection over x-axis
2. 180 degree rotation
3. Reflection over y-axis
4. Translation
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Answer: 180 degree rotation
180 degree rotation: (x,y) becomes (-x,-y). So (2,3) becomes (-2,-3).
After 180 degree rotation about origin, (-1, 4) maps to:
1. (1, -4)
2. (-1, -4)
3. (4, -1)
4. (-4, 1)
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Answer: (1, -4)
180 degree rotation: (-1,4) becomes (1,-4).
A dilation produces a figure similar (same shape, different size) to the original.
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Answer: True
Dilations produce similar figures — same angle measures and proportional sides.

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