Coordinate changes | Year 6

01 / LEARN

Understand the idea.

Change one coordinate at a time

A horizontal slide changes only $x$ : moving right adds to it and moving left subtracts from it. A vertical slide changes only $y$ : moving up adds to it and moving down subtracts from it. Keep the unchanged coordinate.

A slide may cross an axis, so a coordinate’s sign can change. Starting at $x = - 3$ and moving five units right gives $- 3 + 5 = 2$ . Three units reach zero, and the remaining two continue onto the positive side.

Equal-unit Cartesian grid from −5 to 5 on both axes. Points: A (-3, 1); B (2, -1).

Reflect across an axis

A reflection places a point the same distance on the other side of a mirror. In the $x$ -axis, horizontal position stays fixed and $y$ changes sign: $(x, y) \mapsto (x, - y)$ . In the $y$ -axis, $x$ changes sign: $(x, y) \mapsto (- x, y)$ .

A point on the mirror axis stays in place because its distance from the mirror is zero. For a shape, apply the same move to every vertex, then join the corresponding vertices in order. Reflections and slides preserve lengths.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A slide crossing both axes

A point starts at (−3,1). Move it 5 units right and 2 units down. Find the result.

Worked solution

1
Apply the horizontal slide.
$x = - 3 + 5 = 2$
Moving right increases the horizontal coordinate, including when the move crosses zero.
2
Apply the vertical slide.
$y = 1 - 2 = - 1$
Moving down decreases the vertical coordinate while leaving the new horizontal coordinate unchanged.
3
Combine the new coordinates.
$(- 3, 1) ⟼ (2, - 1)$
The final point is at horizontal position two and vertical position negative one.

Answer

(2,−1).

EXAMPLE 02

Two reflections

Reflect (−4,3) in the x-axis, then reflect the result in the y-axis.

Worked solution

1
Reflect the original point in the horizontal axis.
$(- 4, 3) ⟼ (- 4, - 3)$
Reflection in the x-axis reverses vertical position but keeps horizontal position.
2
Reflect that image in the vertical axis.
$(- 4, - 3) ⟼ (4, - 3)$
Reflection in the y-axis reverses the new horizontal position but keeps its vertical position.
3
Check the final signs.
$final point = (4, - 3)$
The first reflection changes only the original y sign; the second changes only its x sign.

Answer

(4,−3).

03 / YOUR TURN

Try it yourself.

Check your understanding

Reflect (−2,5) in the y-axis.

Show answer & reasoning

(2,5)

Reflection in the $y$ -axis changes the horizontal coordinate from $- 2$ to $2$ and keeps the height $5$ . The image is $(2, 5)$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

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: $(- 1, 1)$ , $(2, 1)$ , $(2, 3)$ , $(- 1, 3)$ .

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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 ↗

In this lesson

Understand the idea.

Change one coordinate at a time

Reflect across an axis

See the method in action.

A slide crossing both axes

Apply the horizontal slide.

Apply the vertical slide.

Combine the new coordinates.

Two reflections

Reflect the original point in the horizontal axis.

Reflect that image in the vertical axis.

Check the final signs.

Try it yourself.

Check your understanding

Keep practising