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Primary Maths · Year 4Chapter 10 · Position and direction
Year 4 · Coordinates and Translation · Lesson 10.2

Year 4: Plotting points and drawing shapes

Part of the Year 4 coordinates and translation chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)

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10.2

Plotting points and drawing shapes

Year 4
Plot specified points on a grid, Draw sides to complete a given polygon

To plot a point means to mark it on a grid. Here is how to plot the point (3, 2).

  1. Start at the origin, (0, 0).
  2. Go along the x-axis to 3 (the first number).
  3. Go up to 2 (the second number).
  4. Mark the point with a small cross or dot and write its label.
012345612345xyP (3, 2)3 along2 up
Plotting (3, 2): 3 along, then 2 up.

You can make a shape by plotting points and then joining them in order with a ruler. Each corner of the shape is called a vertex. Join the last point back to the first one to close the shape. Then you can name the shape by looking at its sides and its right angles.

012345612345xyABCD
A, B, C and D are plotted and joined in order. The shape has 4 right angles, so it is a rectangle.

Points can also make a straight line. Look at the points below. Every point has a y-coordinate of 3. They make a horizontal (flat) line.

01234567812345xyA (1, 3)B (3, 3)C (5, 3)D (7, 3)y = 3 everywhere01234567812345678xyE (5, 1)F (5, 3)G (5, 5)H (5, 7)x = 5 everywhere
Points on a horizontal line all have the same y-coordinate. Points on a vertical line all have the same x-coordinate.

The points on the second line all have an x-coordinate of 5. They make a vertical (straight up and down) line. A good question to ask is: “What do all the points on this line have in common?”

Key ideas

  • To plot (x, y): start at the origin, go along x, go up y, then mark the point.
  • Join the points in order and join the last one back to the first to make a polygon. Corners are called vertices.
  • Name a shape using its sides and its right angles. Count how long each side is on the grid.
  • Points with the same y are in a horizontal line. Points with the same x are in a vertical line.
Worked example 10.2.1
Plot the point P (3, 2) on the grid.
012345612345xy

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Start at the origin. For each point go along first, then up, and mark it with a cross.

  1. Find the origin. Every point is measured from (0, 0), where the axes meet.
    Put your finger on (0, 0).
  2. Plot P (3, 2). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 3 along the x-axis, then 2 up.
  3. Check the picture. Every point should sit where its along number and up number meet.
    012345612345xyP

Check. Read each point back: look along to its x-coordinate and up to its y-coordinate. They match the numbers in the question. ✓

Watch out. Do not mix up the two numbers: along first, then up.

Worked example 10.2.2
Plot the points A (1, 1), B (4, 1) and C (1, 4). Join them in order and join C back to A. What shape have you drawn?
012345612345xy

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Start at the origin. For each point go along first, then up, and mark it with a cross.

  1. Find the origin. Every point is measured from (0, 0), where the axes meet.
    Put your finger on (0, 0).
  2. Plot A (1, 1). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 1 along the x-axis, then 1 up.
  3. Plot B (4, 1). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 4 along the x-axis, then 1 up.
  4. Plot C (1, 4). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 1 along the x-axis, then 4 up.
  5. Join the points in order with a ruler and close the shape. Join the last point back to the first one.
    012345612345xyABC
    The shape is a right-angled isosceles triangle.

Check. Read each point back: look along to its x-coordinate and up to its y-coordinate. They match the numbers in the question. ✓

Watch out. Do not mix up the two numbers: along first, then up.

Worked example 10.2.3
Plot the points A (2, 2), B (6, 2), C (6, 5) and D (2, 5). Join them in order. What shape is it?
01234567123456xy

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Start at the origin. For each point go along first, then up, and mark it with a cross.

  1. Find the origin. Every point is measured from (0, 0), where the axes meet.
    Put your finger on (0, 0).
  2. Plot A (2, 2). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 2 along the x-axis, then 2 up.
  3. Plot B (6, 2). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 6 along the x-axis, then 2 up.
  4. Plot C (6, 5). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 6 along the x-axis, then 5 up.
  5. Plot D (2, 5). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 2 along the x-axis, then 5 up.
  6. Join the points in order with a ruler and close the shape. Join the last point back to the first one.
    01234567123456xyABCD
    The shape is a rectangle.

Check. Read each point back: look along to its x-coordinate and up to its y-coordinate. They match the numbers in the question. ✓

Watch out. Do not mix up the two numbers: along first, then up.

Worked example 10.2.4
Write the coordinates of the corners of the square.
012345612345xyABCD

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Read each corner (vertex) of the shape on its own. For every corner, go along first and then up.

  1. Look at the first corner. Start at the origin for every corner. Look down to the x-axis, then across to the y-axis.
    A: along 2, up 1 → (2, 1)
  2. Do the same for the other corners. Along first, then up, every time.
    B: along 5, up 1 → (5, 1)
    C: along 5, up 4 → (5, 4)
    D: along 2, up 4 → (2, 4)
  3. Write the answer. List the corners in order.
    A (2, 1), B (5, 1), C (5, 4), D (2, 4)
    012345612345xyABCD

Check. Plot the points again: they land on the corners of the shape. ✓

Watch out. Along first, then up, for every corner.

Worked example 10.2.5
The points A (1, 4), B (3, 4) and C (6, 4) are on a straight line. What do all the points on the line have in common?
01234567123456xyABC

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Write down the coordinates of all the points. Look for a number that is the same in every pair.

  1. Write the coordinates of every point. Read each point: along first, then up.
    A = (1, 4)
    B = (3, 4)
    C = (6, 4)
  2. Look at the second numbers. The second number is the y-coordinate. Do they match?
    4, 4, 4
    They are all 4.
  3. Say what they have in common. A line of points that share a y-coordinate is horizontal (flat).
    Every point has y = 4, so the points are on a horizontal line.
    01234567123456xyABC

Check. Every point has y-coordinate 4, so the line is flat. ✓

Watch out. The y-coordinate is the second number. A flat line has the same y-coordinate everywhere.

Worked example 10.2.6
The points P (5, 1), Q (5, 3) and R (5, 6) are on a straight line. What do all the points have in common?
012345671234567xyPQR

Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.

Method. Write down the coordinates of all the points. Look for a number that is the same in every pair.

  1. Write the coordinates of every point. Read each point: along first, then up.
    A = (5, 1)
    B = (5, 3)
    C = (5, 6)
  2. Look at the first numbers. The first number is the x-coordinate. Do they match?
    5, 5, 5
    They are all 5.
  3. Say what they have in common. A line of points that share a x-coordinate is vertical (straight up and down).
    Every point has x = 5, so the points are on a vertical line.
    012345671234567xyABC

Check. Every point has x-coordinate 5, so the line is straight up. ✓

Watch out. The x-coordinate is the first number. A line going straight up has the same x-coordinate everywhere.

Worked example 10.2.7
Plot A (1, 1), B (5, 1), C (5, 4), D (3, 6) and E (1, 4). Join them in order and close the shape. How many sides does it have, and what is it called?
01234561234567xy

Key words. To plot a point means to mark it on a grid with a small cross or dot. A vertex is a corner of a shape (more than one are called vertices). A polygon is a flat shape with straight sides.

Method. Start at the origin. For each point go along first, then up, and mark it with a cross.

  1. Find the origin. Every point is measured from (0, 0), where the axes meet.
    Put your finger on (0, 0).
  2. Plot A (1, 1). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 1 along the x-axis, then 1 up.
  3. Plot B (5, 1). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 5 along the x-axis, then 1 up.
  4. Plot C (5, 4). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 5 along the x-axis, then 4 up.
  5. Plot D (3, 6). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 3 along the x-axis, then 6 up.
  6. Plot E (1, 4). The first number is along, the second number is up. Then mark the point with a small cross.
    Go 1 along the x-axis, then 4 up.
  7. Join the points in order with a ruler and close the shape. Join the last point back to the first one.
    01234561234567xyABCDE
    The shape is a pentagon (5 sides).

Check. Read each point back: look along to its x-coordinate and up to its y-coordinate. They match the numbers in the question. ✓

Watch out. Do not mix up the two numbers: along first, then up.

Watch out

Plot along first, then up. To plot (4, 2), go 4 along and 2 up, not 2 along and 4 up. When you join points, join them in the order given. Joining them in a different order can make a different shape.

Exercise 10B  Plotting points and drawing shapes

Non-calculator
1
FPlot each point on the grid. Label it with its letter.
0123456123456xy
(a)A (2, 4)
(b)B (5, 1)
(c)C (0, 3)
(d)D (6, 6)
2
FPlot the points A (1, 1), B (5, 1), C (5, 4) and D (1, 4). Join them in order and join D back to A. What shape have you drawn?
012345612345xy
3
FPlot P (1, 1), Q (5, 1) and R (1, 4). Join them in order and join R back to P. What shape have you drawn?
012345612345xy
4
FPlot A (2, 2), B (5, 2), C (5, 5) and D (2, 5). Join them in order. What is the name of the shape?
0123456123456xy
5
FPlot A (1, 1), B (5, 1), C (7, 4) and D (3, 4). Join them in order. What is the name of the shape? (Hint: look at the two pairs of sides that slant the same way.)
01234567812345xy
6
FLook at the shape on the grid.
012345612345678xyABCD
(a)Write the coordinates of A, B, C and D.
(b)What is the name of the shape?
7
FPlot A (2, 1), B (6, 1) and C (4, 5). Join them in order and close the shape. What is the name of the triangle? (Two sides slant the same amount.)
01234567123456xy
8
PSPlot A (1, 1), B (5, 1), C (5, 2), D (2, 2), E (2, 6) and F (1, 6). Join them in order and close the shape. It looks like a letter. Which letter is it? How many sides has it got?
01234561234567xy
9
RWhat do all the points on each line have in common?
(a)The points (1, 6), (3, 6), (5, 6) and (8, 6) are on a line.
(b)The points (2, 1), (2, 4) and (2, 7) are on a line.
10
RThe points (1, 3) and (2, 3) are on a horizontal line. Write the coordinates of two more points on the same line.
012345678123456xy(1, 3)(2, 3)
11
RRavi has been asked to plot (4, 2). He puts a cross at X. What mistake has he made?
0123456123456xyX
12
RJack plots A (1, 2), B (4, 2), C (4, 6) and D (1, 6) and joins them in order. He says, “I have drawn a square.” Is Jack right? Explain how you know.
01234561234567xy
13
RWrite always, sometimes or never for each sentence.
(a)Points with the same y-coordinate are on a horizontal line.
(b)A shape drawn on a grid with four right angles is a square.
(c)The points (1, 2), (2, 3) and (3, 4) are on a horizontal line.
14
PSPlot A (2, 1), B (6, 1), C (6, 4) and D (2, 4) and join them to make a rectangle. Each side of a grid square is 1 cm long. What is the perimeter of the rectangle?
01234567123456xy

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