Geometry Transformation Quiz
Questions: 16 · 10 minutes
1. A quarter-turn counterclockwise about the origin is applied to (2, -5). Which landing point is correct?
(-5, -2), from exchanging the coordinates without the required sign change
(-2, 5), from changing both signs but keeping the coordinate order
(5, 2), from applying the rule (x, y) → (-y, x)
(2, 5), from changing only the vertical sign
2. Which coordinate rule represents a reflection across the diagonal line y = x?
Swap the coordinates: x′ = y and y′ = x
Keep x and reverse the sign of y: x′ = x and y′ = -y
Reverse the sign of x and keep y: x′ = -x and y′ = y
Swap the coordinates and reverse both signs: x′ = -y and y′ = -x
3. A point lies 6 units from the center of a dilation. If the scale factor is 0.5, how far from the center is its image?
12 units
6.5 units
5.5 units
3 units
4. The vertical line x = 2 is the perpendicular bisector between a point at (5, -1) and its reflected image. Which location is the image?
(1, -1), which is one unit left of the mirror line
(-5, -1), which reverses the original horizontal coordinate sign
(-1, -1), which is three units left of the mirror line
(5, 5), which changes the vertical coordinate instead
5. A translation moves the point (-3, 2) to (4, -1). Which translation rule was used?
Add 1 to x and subtract 5 from y
Subtract 7 from x and add 3 to y
Add 7 to x and subtract 3 from y
Subtract 1 from x and add 5 to y
6. A dilation centered at the origin has a scale factor of 2. What is the image of (-1, 3)?
(-2, 6)
(1, -3)
(-0.5, 1.5)
(-1, 6)
7. A point has coordinates (5, -7). After the plane is reflected across the x-axis, which coordinates describe the image?
(-5, -7), because only the x-coordinate changes sign
(7, 5), because the coordinates exchange places and both signs change
(-5, 7), because both coordinate signs change
(5, 7), because only the y-coordinate changes sign
8. A dilation centered at the origin maps (2, -3) to (6, -9). What is its scale factor?
One-third
2
6
3
9. A polygon's vertices are listed clockwise. Which single transformation makes the corresponding image vertices run counterclockwise?
A rotation
A translation
A reflection
A dilation with a positive scale factor
10. A translation using the rule (x, y) → (x - 4, y + 5) produces the image point (2, 1). What was the preimage?
(-2, 6)
(6, -4)
(-2, -4)
(6, 6)
11. A half-turn about the origin sends a point to (6, -4). Where was the point before the rotation?
(-6, 4), since a half-turn reverses both coordinate signs
(6, 4), since a half-turn reverses only the vertical sign
(-4, 6), since a half-turn exchanges the coordinates
(4, -6), since a half-turn exchanges the coordinate values and signs
12. Which transformation is always a rigid transformation?
A dilation with scale factor 2
A translation
A horizontal stretch
A shear
13. A figure is reflected across the x-axis and then across the y-axis. Which single transformation about the origin has the same effect?
A 90-degree clockwise rotation
A reflection across y = x
A translation by (-1, -1)
A 180-degree rotation
14. A triangle is rotated 90 degrees about a point. Which statement about the image must be true?
It is congruent to the original triangle
It is similar to the original but cannot be congruent to it
Its area is half the area of the original triangle
Its orientation is reversed
15. A figure is translated 3 units right and 2 units up, then 5 units left and 1 unit down. Which single translation has the same effect?
8 units right and 3 units up
2 units left and 1 unit up
2 units right and 1 unit down
8 units left and 1 unit up
16. Which property is preserved by every dilation with a positive scale factor?
Corresponding side lengths
Corresponding angle measures
Area
Perimeter