Rules & Patterns
What stays the same when a shape is translated?
Shape, size, orientation
Translate the point (2, 5) 3 units left and 2 units down. What are the new coordinates?
(–1, 3)
What happens to the y-coordinate when a point is reflected over the x-axis?
It changes sign: y → –y
What happens to the x- and y-coordinates when a point is rotated 180° about the origin?
(x, y) → (–x, –y)
Does translating a shape change its size or orientation? Explain.
No, it only moves the shape; size and orientation stay the same.
Write the translation rule if a point moves 3 right and 5 up.
(x, y) → (x + 3, y + 5)
Translate the square with vertices A(0,0), B(0,2), C(2,2), D(2,0) 4 right.
A(4,0), B(4,2), C(6,2), D(6,0)
Reflect the point (–3, 6) over the y-axis. What are the new coordinates?
(3, 6)
Rotate the point (–3, 6) 90° CCW about the origin. What are the new coordinates?
(–6, –3)
Does reflecting a shape over a line change its size? Explain.
No, size stays the same; the image is flipped across the line.
If a point is reflected across the y-axis, write the rule for its new coordinates.
(x, y) → (–x, y)
Point P(–3, 7) translates 5 down and 2 right. New coordinates?
P’(–1, 2)
Reflect triangle A(2,3), B(5,1), C(3,6) over y = –2. List the new coordinates.
A’(2,–7), B’(5,–5), C’(3,–10)
Rotate the triangle with vertices A(1,4), B(4,2), C(2,7) 90° CCW about the origin. List the new coordinates.
A’(–4,1), B’(–2,4), C’(–7,2)
Does rotating a shape around a point change its size or shape? Why?
No, rotation preserves size and shape; it only changes orientation.
Write the rule for rotating a point 90° counterclockwise about the origin.
(x, y) → (–y, x)
Write the translation rule for a shape that moves 6 left and 3 up.
(x – 6, y + 3)
Write the rule for reflecting a point over x = 4.
(8 – x, y)
Rotate quadrilateral K(2,–5), L(5,–5), M(2,0), N(5,0) 180° about the origin. New coordinates?
K’(–2,5), L’(–5,5), M’(–2,0), N’(–5,0)
After reflecting a shape over the x-axis, what changes?
The y-coordinates change sign; shape orientation flips vertically.
A triangle is reflected over y = –2 and then translated 3 right and 4 up. Write a combined transformation rule.
(x + 3, y = [-2 + change] + 4)
Translate triangle M(1,2), N(4,1), O(2,5) 3 left and 7 down. List the new coordinates.
M’(–2,–5), N’(1,–6), O’(–1,–2)
Reflect quadrilateral P(1,2), Q(4,2), R(4,5), S(1,5) over x = 3. Write new coordinates.
P’(5,2), Q’(2,2), R’(2,5), S’(5,5)
Rotate triangle P(1,2), Q(4,2), R(2,5) 90° CCW around vertex P(1,2). Write the new coordinates.
P’(1,2), Q’(1,5), R’(–2,4)
Explain the direction of rotation for a 270° CW rotation.
270° CW is the same as 90° CCW; rotation moves points clockwise around the centre.