The idea, step by step
Change one coordinate at a time
A horizontal slide changes x but not y. Moving right increases x; moving left decreases x. A vertical slide changes y but not x. Moving up increases y; moving down decreases y.
You can cross an axis during a slide. From x = −3, moving 5 units right gives x = 2. Count through zero or calculate −3 + 5 = 2.
Reflect across an axis
Reflecting in the x-axis keeps the horizontal position and reverses the vertical position. For example, (3,−2) becomes (3,2). Reflecting in the y-axis reverses the horizontal position and keeps the vertical position.
A point on the mirror axis stays where it is. For a shape, apply the same change to every vertex, then reconnect matching vertices. Check that its size has not changed.
A common trap
Changing both signs for a reflection in just one axis.
Instead: Only the coordinate perpendicular to the mirror changes sign: y for the x-axis, x for the y-axis.
See the thinking
A slide crossing both axes
A point starts at (−3,1). Move it 5 units right and 2 units down. Find the result.
- New x = −3 + 5 = 2.
- New y = 1 − 2 = −1.
Two reflections
Reflect (−4,3) in the x-axis, then reflect the result in the y-axis.
- First reflection reverses y: (−4,−3).
- The second reverses x: (4,−3).
Check your understanding
Reflect (−2,5) in the y-axis.
Show answer
(2,5)
The horizontal position reverses; the vertical position stays 5.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Move (2,−3) 1 unit left and 5 units up.2 marks
- Move (−4,−1) 2 units right and 3 units up.2 marks
- Reflect (3,−2) in the x-axis.1 mark
- Reflect (−1,4) in the y-axis.1 mark
- Describe one horizontal move and one vertical move taking A = (−3,−2) to B = (2,1).2 marks
- A rectangle has vertices (−4,−1), (−1,−1), (−1,1), (−4,1). Slide it 3 units right and 2 units up. Plot the image.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Move (2,−3) 1 unit left and 5 units up.2 marks
2 − 1 = 1; −3 + 5 = 2.
(1,2) - Move (−4,−1) 2 units right and 3 units up.2 marks
−4 + 2 = −2; −1 + 3 = 2.
(−2,2) - Reflect (3,−2) in the x-axis.1 mark
Keep x = 3 and reverse the sign of y.
(3,2) - Reflect (−1,4) in the y-axis.1 mark
Reverse the sign of x and keep y = 4.
(1,4) - Describe one horizontal move and one vertical move taking A = (−3,−2) to B = (2,1).2 marks
Horizontal change: 2 − (−3) = 5.
Vertical change: 1 − (−2) = 3.
5 units right and 3 units up. - A rectangle has vertices (−4,−1), (−1,−1), (−1,1), (−4,1). Slide it 3 units right and 2 units up. Plot the image.3 marks
Add 3 to every x-coordinate.
Add 2 to every y-coordinate.
Reconnect the points in the same order.
New vertices: (−1,1), (2,1), (2,3), (−1,3).
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 6 four-quadrant Cartesian coordinates, plotting and reading points, and coordinate changes.
Official curriculum source ↗