YEAR 7 · COORDINATES, PATTERNS AND GRAPHS · 15 MIN

Reading and plotting points

Read labelled points accurately and plot ordered pairs on a grid.

In this lesson

Read coordinates from grid lines
Plot points and check each coordinate

Before you start

Ordered pairs
Four quadrants

01 / LEARN

Understand the idea.

Read the dot, not its label

The dot fixes the position; the nearby letter only names it. Check the numbered ticks to find the value of each grid interval. Read the dot horizontally against the $x$ -axis scale and vertically against the $y$ -axis scale.

On the supplied grid each interval represents one unit. Point $P$ is aligned with $x = - 4$ and $y = 1$ , so its ordered pair is $(- 4, 1)$ . Use the dot rather than the centre of its printed label.

Square coordinate grid from minus five to five on both axes. P is minus four-one, Q is two-three, R is three-minus two and S is zero-minus three.

Plot and check

To plot $(x, y)$ , begin at the origin and move horizontally to $x$ . From there, move parallel to the vertical axis until you reach height $y$ . Mark the intersection with a small dot and place its letter beside it.

Read the finished dot back as an ordered pair to check both coordinates and signs. If a label overlaps another mark, move the label rather than shifting the dot away from its correct position.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read a plotted point

Read Q in the supplied grid.

Worked solution

1
Read the horizontal position of Q.
$x = 2$
The dot is aligned with the tick 2 on the horizontal scale.
2
Read the vertical position of Q.
$y = 3$
The dot is aligned with the tick 3 on the vertical scale.
3
Write the coordinates in order.
$Q = (2, 3)$
The horizontal coordinate is always written before the vertical coordinate.

Answer

$Q = (2, 3)$

EXAMPLE 02

Plot below the axis

Plot $T = (- 2, - 1)$ .

Square coordinate grid from minus five to five on both axes, with T plotted at minus two-minus one.

Worked solution

1
Locate the horizontal position.
$x = - 2$
From the origin, move 2 units left along the horizontal axis.
2
Locate the required height.
$y = - 1$
From that position, move 1 unit down, keeping the horizontal coordinate at -2.
3
Mark and check the point.
$T = (- 2, - 1)$
The dot must be 2 units left and 1 unit below the origin; write T beside it.

Answer

$T = (- 2, - 1)$

03 / YOUR TURN

Try it yourself.

Check your understanding

A point is on the y-axis 3 units below the origin. What are its coordinates?

Show answer & reasoning

$(0, - 3)$

Being on the $y$ -axis fixes $x = 0$ . Three units below the origin means $y = - 3$ , so the point is $(0, - 3)$ .

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

Read P.
2 marks
Read R.
2 marks
Plot $A = (- 3, 4)$ and $B = (2, - 4)$ .
3 marks
Write the coordinates of the point on the x-axis 5 units left of the origin.
2 marks
Mina plots $(1, - 3)$ as 1 down and 3 right. Give the coordinates she plotted, then correct her moves.
3 marks
What do $U = (- 2, 3)$ and $V = (4, 3)$ have in common?
2 marks

Read the worked solutions

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

Read P.
2 marks
P is 4 left and 1 up.
$(- 4, 1)$
Read R.
2 marks
R is 3 right and 2 down.
$(3, - 2)$
Plot $A = (- 3, 4)$ and $B = (2, - 4)$ .
3 marks
For A: left 3, up 4.
For B: right 2, down 4.
A at $(- 3, 4)$ ; B at $(2, - 4)$ .
Write the coordinates of the point on the x-axis 5 units left of the origin.
2 marks
Left gives $x = - 5$ . On the x-axis gives $y = 0$ .
$(- 5, 0)$
Mina plots $(1, - 3)$ as 1 down and 3 right. Give the coordinates she plotted, then correct her moves.
3 marks
Her horizontal move is 3; her vertical move is -1.
The intended coordinates reverse these roles.
She plotted $(3, - 1)$ . Correct: 1 right and 3 down.
What do $U = (- 2, 3)$ and $V = (4, 3)$ have in common?
2 marks
Their y-coordinates match.
They have the same height and lie on $y = 3$ .

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9.0 / South Australian Curriculum

Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.

Official curriculum source ↗

In this lesson

Understand the idea.

Read the dot, not its label

Plot and check

See the method in action.

Read a plotted point

Read the horizontal position of Q.

Read the vertical position of Q.

Write the coordinates in order.

Plot below the axis

Locate the horizontal position.

Locate the required height.

Mark and check the point.

Try it yourself.

Check your understanding

Keep practising