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4.3 B) Reflection: Undertaking – Part 2
4.3 B) Reflection: Undertaking – Part 2
The content in this section builds on the content that was discussed in the previous section. Make sure that you have covered the content in the previous section before working through the content in this section (click here to be taken through to the content in the previous section).
Reflection questions can be made harder by having a mirror line that is upwards or downwards sloping. We are going to be looking at these types of reflections in this section.
Reflection questions can be made harder by having a mirror line that is upwards or downwards sloping. We are going to be looking at these types of reflections in this section.
Example 1
There is a shape drawn on the grid below.
There is a shape drawn on the grid below.
Reflect this shape through the given mirror line. Click here for a printable version of the examples in this section.
The working is exactly the same as the working for the examples in the previous section. The first step 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 have been drawn on the grid below.
The working is exactly the same as the working for the examples in the previous section. The first step 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 have been drawn on the grid below.
The distances between the points on the shape and the mirror line will be the same as the distances between the respective points on the image and the mirror line. Let’s have a look at the point labelled A. We want to find the distance between point A and the mirror line. The easiest way to find this distance is to split it up into a horizontal and vertical distance. The horizontal distance between point A and the mirror line is 3 and the vertical distance is also 3.
We know that the distance between the respect point on the image (A’) and the mirror line will be the same. Therefore, we move 3 squares to the right (horizontal distance) and then 3 squares down (vertical distance). Point A’ is shown on the diagram below.
We do the same for the other 2 points:
The outcome is shown below.
- The distance between point B and the mirror line is 2.5 squares horizontally and 2.5 vertically. This means that the distance between B’ and the mirror line will be 2.5 squares horizontally and 2.5 vertically.
- The distance between point C and the mirror line is 0.5 squares horizontally and 0.5 vertically. This means that the distance between C’ and the mirror line will be 0.5 squares horizontally and 0.5 vertically.
The outcome is shown below.
Example 2
Sometimes it may be the case that you are given the equation of the mirror line. The first step in answering these types of questions is to plot the mirror line. After the mirror line has been plotted, we answer the question in the usual way.
Reflect the shape below in the line y = x – 3.
Sometimes it may be the case that you are given the equation of the mirror line. The first step in answering these types of questions is to plot the mirror line. After the mirror line has been plotted, we answer the question in the usual way.
Reflect the shape below in the line y = x – 3.
The first step in answering this question is to draw the mirror line on the graph. The mirror line has the equation y = x – 3. We are able to plot this line by subbing in a few different values for x. I am going to sub x in as 0 and 2 (we could choose any x values).
We get the coordinates (0, -3) and (2, -1). We plot these two points on the graph and draw a straight line passing through these two points. The line is drawn on the graph below.
We now reflect the shape in the usual way. We draw lines going from the points on the shape to and through the mirror line.
We now make sure that the distance between the points on the shape and the mirror line are the same as the distances between the respective points on the image and the mirror line. We then connect all of the points to create the shape. The shape is shown on the diagram below.
Example 3
Sometimes it will be the case that we have a mirror line that passes through the shape. These questions are a little strange, but the process in answering them is exactly the same as all of the previous questions.
Reflect the shape below through the line y = -x + 1.
Sometimes it will be the case that we have a mirror line that passes through the shape. These questions are a little strange, but the process in answering them is exactly the same as all of the previous questions.
Reflect the shape below through the line y = -x + 1.
The first step is to draw the mirror line on the diagram. The equation for the mirror line is y = -x + 1. We can plot this line by subbing in two different values of x. I am going to sub x as 0 and 2.
This tells us that the coordinates of two points on the line are (0, 1) and (2, -1). We now plot these two points and draw a straight line passing through them.
We now reflect in the usual way by drawing perpendicular lines going from each of the points on the shape to the mirror line. For this shape, 3 of the perpendicular lines will be downwards sloping and these will be from the points A, B and C. One of the perpendicular lines will be upwards sloping and this is the perpendicular line from point D. The perpendicular lines are shown on the diagram below.
The next step is to make sure that the distances between the points on the shape and the mirror line are the same as the distances between the respective points on the image and the mirror line. The process is exactly the same for all of the points despite A, B and C being on one side of the mirror line and D being on the other side of the mirror line.
The final step is to connect the points to create the image. The image is shown in green on the diagram below.
The final step is to connect the points to create the image. The image is shown in green on the diagram below.