Translation — Grade 8 Math, what it means and where it is taught
A slide. Every point moves the same distance in the same direction.
Taught in Grade 8 Math.
Where it is taught
Practise this idea
4 questions in the course bank use Translation, in Translations, Reflections & Rotations.
Problem 1
A triangle has vertices (1, 1), (4, 1), (4, 5). After a translation, the image of (1, 1) is (-2, 6). Where does (4, 5) go?
Worked answer
(1, 10)
1 → -2 means -3 on x
1 → 6 means +5 on y
(4 - 3, 5 + 5) = (1, 10)
Problem 2
A figure is moved so that every point travels 6 units right and 0 units vertically. Which is true of the image?
- It is congruent to the original
- It is larger than the original
- It is a mirror image of the original
- It has different angle measures
Worked answer
It is congruent to the original
A translation changes position only
Lengths and angles are unchanged
So the image is congruent
Problem 3
A point is reflected across the y-axis and then translated 4 right. The final image is (1, 6). Find the original point.
Worked answer
(3, 6)
Undo the translation: (1 - 4, 6) = (-3, 6)
Undo the reflection: (3, 6)
Check: (3,6) → (-3,6) → (1,6) ✓
Problem 4
A translation of 3 right and 2 up is followed by another of 1 left and 5 down. Write the single rule that does both.
Worked answer
(x + 2, y - 3)
Horizontal: +3 - 1 = +2
Vertical: +2 - 5 = -3
(x, y) → (x + 2, y - 3)