Plotting/reading points | Year 6

01 / LEARN

Understand the idea.

Read across, then up or down

An ordered pair always records horizontal position before vertical position: $(x, y)$ . To read a point, project it straight down or up to the $x$ -axis, then across to the $y$ -axis. Keep each coordinate’s sign.

Read the scale before counting grid spaces. Here each interval is one unit; on another grid an interval might represent two or five units. Count units from the origin, not simply the number of lines visible beside a point.

Equal-unit Cartesian grid from minus five to five on both axes, with A at minus four, one and B at two, minus three.

Plot and check

To plot a point, start at $(0, 0)$ . Move horizontally for the first coordinate, then vertically for the second. Mark the intersection clearly and place its letter slightly to one side so the point itself remains visible.

Check a plotted point by reading its coordinates back from the axes. For $(3, 2)$ , the horizontal position must be three right and the vertical position two up. Swapping the coordinates would give a different point, $(2, 3)$ .

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read point A

Read the coordinates of A on the grid.

Worked solution

1
Read A’s horizontal position.
$x = - 4$
The grid has one-unit intervals, and A is four units left of the origin.
2
Read A’s vertical position.
$y = 1$
A is one unit above the horizontal axis.
3
Write the pair in coordinate order.
$A = (- 4, 1)$
Horizontal position comes first, followed by vertical position.

Answer

A = (−4,1).

EXAMPLE 02

Plot a point

Plot C = (3,2).

Equal-unit Cartesian grid from minus five to five on both axes, with C at three, two.

Worked solution

1
Move horizontally from the origin.
$(0, 0) ⟼ (3, 0)$
The first coordinate is positive three, so move three units right.
2
Move vertically to the requested height.
$(3, 0) ⟼ (3, 2)$
The second coordinate is positive two, so move two units up without changing the horizontal position.
3
Mark and label the intersection.
$C = (3, 2)$
The labelled point is three units right and two units up from the origin, as required.

Answer

C is 3 right and 2 up from the origin.

03 / YOUR TURN

Try it yourself.

Check your understanding

A point is 2 units left and 4 units up from the origin. Give its coordinates.

Show answer & reasoning

(−2,4)

Two units left gives $x = - 2$ and four units up gives $y = 4$ . Writing horizontal before vertical gives $(- 2, 4)$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Read the coordinates of B on the grid.
1 mark
Plot $P = (- 2, 4)$ on the grid.
2 marks
Plot $Q = (4, - 1)$ on the grid.
2 marks
Plot $P = (- 3, - 2)$ , $Q = (1, - 2)$ and $R = (1, 2)$ . Join P to Q, Q to R and R to P.
3 marks
For $(2, - 4)$ , Sam moves 4 units left and 2 units up. Explain and correct the plotting error.
2 marks
Give the coordinates of a point on the $x$ -axis 5 units left of the origin.
1 mark

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Read the coordinates of B on the grid.
1 mark
B is 2 right and 3 down from the origin.
$(2, - 3)$
Plot $P = (- 2, 4)$ on the grid.
2 marks
Use $x = - 2$ , then $y = 4$ .
P is 2 left and 4 up from the origin.
Plot $Q = (4, - 1)$ on the grid.
2 marks
Use $x = 4$ , then $y = - 1$ .
Q is 4 right and 1 down from the origin.
Plot $P = (- 3, - 2)$ , $Q = (1, - 2)$ and $R = (1, 2)$ . Join P to Q, Q to R and R to P.
3 marks
P and Q share $y = - 2$ .
Q and R share $x = 1$ .
Join the vertices in the stated order.
The three points form a triangle with a horizontal side PQ and a vertical side QR.
For $(2, - 4)$ , Sam moves 4 units left and 2 units up. Explain and correct the plotting error.
2 marks
The first coordinate, 2, is the horizontal move.
The second coordinate, $- 4$ , is the vertical move.
Sam used the wrong direction and swapped the values. Move 2 right and 4 down.
Give the coordinates of a point on the $x$ -axis 5 units left of the origin.
1 mark
Five left gives $x = - 5$ .
On the $x$ -axis, $y = 0$ .
$(- 5, 0)$

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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.

Read across, then up or down

Plot and check

See the method in action.

Read point A

Read A’s horizontal position.

Read A’s vertical position.

Write the pair in coordinate order.

Plot a point

Move horizontally from the origin.

Move vertically to the requested height.

Mark and label the intersection.

Try it yourself.

Check your understanding

Keep practising