s.html Year 9 Mathematics Transformations

Learning Intentions – Understand what is meant by a transformation – Understand what is meant by reflection Be able to use and find a mirror line Understand what is meant by line symmetry – Understand what is meant by translation Be able to use and find a translation vector – Understand what is meant by rotation Be able to find the centre and angle of rotation – Understand what is meant by enlargement Be able to find the centre and size of enlargement Understand what is meant by rotational symmetry

Transformations In mathematics when a shape is transformed, it is changed The actual shape remains the same, but it might be moved, reflected, enlarged in size, reduced in size or rotated

Reflection When you look at yourself in a mirror, you see a reflection of yourself. Whatever is on the left appears on the right. Whatever is on the right appears on the left Things that are close to the mirror appear close in the reflection Things that are far from the mirror appear far away in the reflection A mirror line is a line drawn between the object and the image

Reflection Reflect this image in the mirror line This mirror line is referred to as x = 3

Reflection Example Reflect this shape in the line y = 4

Reflection Example Reflect this shape in the line y = x

Reflection Example Draw the mirror line that the shape A has been reflected in and give its equation. A

Translation With translation, a shape is moved to the left, right, up or down We use a translation vector to describe the movement. The translation vector indicates how far the shape is moved to the right and how far the shape is moved up This vector indicates that the shape move 4 squares to the right and 1 square down. >> link to MyMathsMyMaths

Translation Example Translate the following shape using the vector

Translation What is the translation vector that maps shape A to shape B A B

Rotation Rotation is when a shape is turned If the shape is turned anticlockwise, the angle is positive If the shape is turned clockwise the angle is negative The point that is used to rotate the shape is called the centre of rotation

Rotation Example Rotate this shape 90 O clockwise about the point (2, 2)

Rotation Example Find the centre of rotation and the angle of rotation to map shape A to shape B A B

Rotational Symmetry A shape has Rotational Symmetry if it still looks the same after it has been turned. The order of rotational symmetry is the number of times it will fit on itself as it is rotated. This star has rotational symmetry of order 5. We can calculate the order using this following formula: A square has rotational symmetry of order 4 – We rotate it 90 O to the first fit

Enlargement With enlargement, a shape is changed in size The shape may be made larger or smaller We use the scale factor to indicate the size of the enlargement If the scale factor is larger than 1, the shape gets bigger If the scale factor is less than 1, the shape gets smaller The centre of enlargement is the point where the enlargement starts

Enlargement Example Enlarge this shape using a scale factor 2 from the origin (0, 0)

Enlargement Example Find the scale factor and the centre of enlargement that maps shape A to shape B A B

Travel Graphs Travel graphs are line graphs that are used to describe the motion of objects such as cars, trains, walkers and cyclists. The distance travelled is represented on the y-axis and the time taken to travel that distance is represented on the x-axis

Example Travel Graph Consider a car travelling at a steady 22m/s (about mph) We represent this on the graph as shown:

Using a Travel Graph If we are given the travel graph already drawn we can take information from it.

Using a Travel Graph Use the travel graph to calculate: – The total distance travelled is _______m – The total time taken is ____s – The distance travelled after two seconds is _______ m – The distance travelled in one second is ________m. i.e. the speed is ______m/s – It takes _________ s to travel 120m.

Some More Travel Graphs

Drawing a Travel Graph When Drawing Travel graphs REMEMBER: – Distance on y-axis – Time on x-axis – Remember units – Plot the time and distance you know and join through 0. – Remember to STOP at total distance/total time – If you are given a SPEED remember this is the distance travelled in ONE unit of time

Drawing a Travel Graph E.G Jodie walks at 5mph for 4 hours. Draw her travel graph and use it to find how far she has walked in 1.5 hours

How Quick … We can calculate the speed using the formula speed = distance ÷ time Example: – How fact is a car travelling if it goes 120 miles in 2 hours? – How far did a car go if it was travelling at 50km/h for 2 hours? d st

What if I Stop? If a vehicle stops on a journey, the distance does not increase and we have a horizontal line. For example: – A car leaves Alford at 10am and travels to Bedford, a distance of 20 km, in 30 minutes. – It stops at Bedford for 15 minutes – It then continues on to arrive at Catford, 25 kilometres from Bedford, arriving at – It remains at Catford until and drives back to Alford, arriving at

Draw the Graph! Find – Time of arrival at Bedford. – Distance from Alford to Catford. – How long at Catford? – Average speed: Alford to Catford. – Average speed for the return journey Time Distance (km) Alford Catford Bedford

Using Travel Graphs How long at Bigby? How far is it from Bigby to Catby? Average speed from Bigby to Catby? Average speed on return journey? Average speed for whole journey? Distance (Miles) Airby Bigby Catby