Mathematics Faculty: Using Autograph
Basic Skills
Open Autograph – if you are asked which version, select STANDARD rather than ADVANCED.
A set of XY-axes will appear on the screen. You are going to start by drawing a shape – Autograph has some pre-set shapes, but your own shape will be more interesting.
Plotting Points
To plot points, go to the ‘Axes’ menu and select ‘Plot points’. Alternatively, click on the yellow cross on the left of the screen. Now plot five points in the top right quadrant.
Click on the white pointer arrow on the toolbar – this stops you accidentally plotting more points. Select all of your points by clicking near your points and dragging a rectangle across them. When you let go, all the points have boxes around them.
If you find this tricky, you can go to the ‘Objects’ menu and choose ‘Select all points’.
To make a shape, right click on your selected points and then choose ‘Group to Shape’.
If you need to move a point, just click on it and move it. The shape will change to match the new position.
If you don’t like your shape, select it and then press the Delete key.
Mini-investigation
Does the order you plot your points affect the final shape?
Transformations: Reflection
Quick question: Imagine a set of co-ordinate axes.
Which one is the X-axis? Which one is the Y-axis?
In order to reflect a shape you need to know where the ‘mirror’ is.
Activity 1
(i) Reflect the shape below in the X-axis. Label the new shape A.
(ii) Reflect the shape below in the Y-axis. Label the new shape B.
To check your answer, look at the shape you made earlier in Autograph.
Select your shape.
Go to the ‘Object’ menu and select ‘Reflection in x-axis’.
Review:
What happens to your original shape?
Is your answer A correct? Do you need to alter your answer for B?
Now select your original shape and repeat for a ‘Reflection in y-axis’.
Challenge: Describe what happens if you reflect your shape in a diagonal line.
Transformations: Rotation
Quick question: Which direction is clockwise?
Activity 1
Rotate this shape through 90˚ (quarter-turn).
Compare your answer to someone else. Do you have identical solutions?
Activity 2:
How can you write more accurate instructions for a Rotation?
How to do rotations in Autograph
1. Open a new page in Autograph.
2. Look at the bottom of the screen. Does it say DEGREES or RADIANS? If it says radians, ask your teacher to change it.
3. Click on the ‘Data’ menu and select ‘Enter shape’. Click on the flag shape and then OK.
4. You need a centre of rotation so put a new point on the origin (0,0).
5. Select the flag and the point (right-click and select all points is the quickest way).
6. Select the ‘Object’ menu and choose ‘Rotation’.
7. Put in an angle of 90˚ and tick the ‘Construction Lines’ box.
8. Click OK.
Activity 1
The original shape is already drawn for you.
Accurately draw the image of this transformation and label it A. Don’t copy the dotted lines.
Repeat this process for 180˚ and 270˚.
Copy the answers from your screen and label them B and C.
Activity 2
Use Autograph to answer these questions. Compare your answers with a partner.
1. What happens if you use -90˚?
What happens if you move the centre of rotation?
What do the construction lines show?
Transformations: Enlargement
Activity 1
Enlarge this shape using a scale factor of 3 – use the grid to help you.
Is your rectangle in the same place as other students?
Setting up the page
· Open a new page in Autograph.
· Change the length of the axes using ‘Edit axes’ from the ‘Axes’ menu. The X-axis is 12. the y-axis is 8.
· Create a Rectangle, using the ‘Object’ menu and ‘Enter shape’. Then type in these co-ordinates:
(1,1), (3,1), (3,2), (1,2)
Question: If you select your Rectangle, then choose the ‘Object’ menu, does the word ENLARGEMENT appear?
Centre of enlargement
To enlarge a shape accurately you must have centre of enlargement.
· Plot a point on the origin.
· Select the point and the rectangle.
· Select ‘Enlargement’ from the ‘Object’ menu.
· Scale factor is 3 and show construction lines.
Carefully draw the image on the axes below. How does it compare to your answer before?
Animation
Autograph will show you how the enlargement is made by animating the process.
· Select the image (new shape).
· Click on the Lightening Flash (or use the right-click menu)
· Click on ‘Animate’ and select ‘Automatic – Repeat’
· Click play.
You can change the speed and enlargement by altering the numbers in the Animate menu.
Activity 2
What happens if you move the centre of enlargement?
What happens if you use a negative scale factor?
What happens if you use a scale factor between 0 and 1?
What happens if you move a corner of the original rectangle?
How do the construction lines help you?
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Mathematics Faculty: Using Autograph
Review questions
Draw each of these questions on squared paper and then check them using Autograph.
Question / Shape / Type / Transformation1 / (1,2), (1, 4), (4, 4) / Reflection / Y-axis
2 / (1,1), (1,2), (2,1), (1,0) / Enlargement / Centre: (-1, -1)
Scale: 2
3 / (1,0), (1,3), (4,3), (2,2) / Rotation / Centre: (0,0)
90˚ clockwise
4 / (1,1), (1,2), (2,3), (3,2), (3,1) / Reflection / X-axis
5 / (1,1), (1,2), (2,2), (3,3), (3,1) / Rotation / Centre: (1,-1)
180˚
6 / (0,0), (2,1), (0,2), (2,2), (2,0) / Enlargement / Centre: (0,3)
Scale: -1
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