Image — Grade 8 Math, what it means and where it is taught
The shape after the move. Its corners get primes: A', B', C'.
Taught in Grade 8 Math.
Where it is taught
Practise this idea
5 questions in the course bank use Image, 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
Point M(2, -3) is rotated 90° counter-clockwise about the origin, then translated 1 unit up. Find the image.
Worked answer
(3, 3)
Rotate: (2, -3) → (3, 2)
Translate up 1: (3, 3)
Problem 4
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 5
Triangle ABC has A(1, 2), B(5, 2), C(1, 6). Its image is A'(2, -1), B'(2, -5), C'(6, -1). Which transformation was used?
Worked answer
rotation of 90 degrees clockwise about the origin
A(1,2) → (2, -1) ✓
B(5,2) → (2, -5) ✓
C(1,6) → (6, -1) ✓
That rule is a 90° clockwise rotation, also called 270° counter-clockwise