Translations, Reflections & Rotations — Drills
Translations, Reflections & Rotations has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Image — The shape after the move. Its corners get primes: A', B', C'.
- Rigid motion — A move that keeps every length and every angle. Slides, flips and turns are all rigid.
- Translation — A slide. Every point moves the same distance in the same direction.
- Reflection — A flip across a line, like a mirror.
- Rotation — A turn about a fixed point, through a given angle and direction.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
- Transformation — A change to the function that moves or stretches its graph.
Translate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Translate (-5, 0) 2 right and 6 up.
Worked answer
(-3, 6)
-5 + 2 = -3
0 + 6 = 6
The image is (-3, 6).
Problem 2
Translate (-1, -2) 6 left and 3 up.
Worked answer
(-7, 1)
-1 - 6 = -7
-2 + 3 = 1
The image is (-7, 1).
Reflect
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Reflect (7, 2) across the x-axis.
Worked answer
(7, -2)
The x stays 7.
The y becomes -2.
The image is (7, -2).
Problem 2
Reflect (-8, -1) across the y-axis.
Worked answer
(8, -1)
The y stays -1.
The x becomes 8.
The image is (8, -1).
Rotate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Rotate (-5, 2) by 180° counter-clockwise about the origin.
Worked answer
(5, -2)
Rule: (x, y) → (-x, -y)
Substitute x = -5, y = 2.
The image is (5, -2).
Problem 2
Rotate (-1, 5) by 90° counter-clockwise about the origin.
Worked answer
(-5, -1)
Rule: (x, y) → (-y, x)
Substitute x = -1, y = 5.
The image is (-5, -1).
Identifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The point (6, 6) maps to (-6, -6). Name the single transformation.
Worked answer
rotation of 180 degrees about the origin
x: 6 → -6
y: 6 → -6
That is a rotation of 180 degrees about the origin.
Problem 2
The point (8, 5) maps to (8, -5). Name the single transformation.
Worked answer
reflection across the x-axis
x: 8 → 8
y: 5 → -5
That is a reflection across the x-axis.
Composing functions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
(5, 1) is reflected across the y-axis, then translated 3 left. Find the image.
Worked answer
(-8, 1)
Reflect: (5, 1) → (-5, 1)
Translate: (-5 - 3, 1)
The image is (-8, 1).
Problem 2
(-5, -1) is reflected across the y-axis, then translated 3 right. Find the image.
Worked answer
(8, -1)
Reflect: (-5, -1) → (5, -1)
Translate: (5 + 3, -1)
The image is (8, -1).