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4.3 K) Multiple Transformations
4.3 K) Multiple Transformations
Sometimes you can be asked questions whereby you are given a series of transformations to undertake. We answer question like this by completing the transformations seperately making sure that we follow the order that we are given them in the question.
Example 1
We are going to perform two transformations on the shape below. Click here for a printable version of this question.
We are going to perform two transformations on the shape below. Click here for a printable version of this question.
Firstly, reflect the shape is the line y = 1. Label this image B. Secondly, enlarge the image by a scale factor of -2 through the point (-1, 3). Label this shape C.
We answer this question by performing the reflection first and then the enlargement. The first step in carrying out the reflection is to draw the line y = 1. This line takes the form of y = “something” and this means that the line is going to be a horizontal line. We draw this line by finding where y is 1 and drawing horizontally across. The line y = 1 is shown on the graph below.
We answer this question by performing the reflection first and then the enlargement. The first step in carrying out the reflection is to draw the line y = 1. This line takes the form of y = “something” and this means that the line is going to be a horizontal line. We draw this line by finding where y is 1 and drawing horizontally across. The line y = 1 is shown on the graph below.
The next step in undertaking a reflection is to draw lines going from the points on the shape to and through the mirror line. These lines need to be perpendicular to the mirror line. These lines are shown on the graph below.
The distances between the points on shape A and the mirror line will be the same as the distances between the respective points on the image and the mirror line. The distance between the top left point and the mirror line is 1 unit. Therefore, the distance between the mirror line and respective point will be 1 unit. This point is shown on the graph below.
We now do the same for the other two points. We then join the points up to create the image and we label this image B.
We are now onto the second transformation, which is an enlargement by a scale factor of -2 through the centre of enlargement (-1, 3). Before we carry out the working for the enlargement, it is worth mentioning that we have a negative scale factor; the scale factor is -2. This means that the enlarged shape will be on the opposite side of the centre of enlargement.
The first step in carrying out an enlargement question is to mark on the graph the centre of enlargement. We are told in the question that the centre of enlargement is (-1, 3) and this is marked on the graph below.
The first step in carrying out an enlargement question is to mark on the graph the centre of enlargement. We are told in the question that the centre of enlargement is (-1, 3) and this is marked on the graph below.
We now draw lines going from each of the points on shape B through the centre of enlargement (we draw the lines through the centre of enlargement because we have a negative scale factor).
I am going to work with the bottom right point on the triangle first (I am going to label this point F). The distance between the centre of enlargement and this point is 1 square to the left and 1 square down. We multiply this distance by -2 to obtain the distance between the centre of enlargement and the point F’ (the respective point to F on the enlarged shape). This results in the distance being 2 to the right and 2 up (the negative on the scale factor results in the direction changing; left become right, and down become up). The point F’ is shown on the graph below.
We do the same with the other two points:
We then join these points together and label the shape C. The final answer is shown on the graph below.
- The distance between the centre of enlargement and the bottom left point (G) is 3 to the left and 1 down. We multiply this distance by -2 to obtain the distance between the centre of enlargement and the point G’, which results in the distance being 6 to the right and 2 up.
- The distance between the centre of enlargement and the top right point (H) is 2 to the left and 2 up. We multiply this distance by -2 to obtain the distance between the centre of enlargement and the point H’, which results in the distance being 4 to the right and 4 down.
We then join these points together and label the shape C. The final answer is shown on the graph below.