Question 1
Translate the shape A by the vector \begin{pmatrix}5\\-4\end{pmatrix}. Label this shape B.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
Our column vector tells us that we go right 5 and down 4. To translate the shape, we choose any point on it, usually a corner.
And then using this point we count right 5 and down 4
And then we need to draw out shape as it was before
Question 2
Reflect shape A in the line y=x
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
To start we need to draw our line of reflection, y=x, which is just a line going diagonally through (0,0), (1,1), (2,2), etc.
Now, we need to see how far away each point is from the line. Starting with one we do it like this:
Start by selecting a point.
We then see how far it is away from the line of reflection
We then map this at the same angle and the same distance from the line
We then repeat this with the other corners of the shape
And once the points have been mapped, we just need to connect them up.
You won’t always need to map all the points, just as many as it takes to see how the shape should be drawn!
Question 3
Describe the translation of shape A to shape B using a column vector.
Select the correct answer from the list below:
A: \begin{pmatrix}-6\\-6\end{pmatrix}
B: \begin{pmatrix}6\\6\end{pmatrix}
C: \begin{pmatrix}-6\\6\end{pmatrix}
D: \begin{pmatrix}6\\-6\end{pmatrix}
CORRECT ANSWER: C: \begin{pmatrix}-6\\6\end{pmatrix}
WORKED SOLUTION:
To determine a translation, we need to select a point on A and the respective point on B. This is usually easiest on a corner that has whole number co-ordinates, so the top corner might be difficult to use.
Now we need to count how many up or down and left or right we go to get from the point on A to the point on B.
So, we go left 6 and up 6, this means our column vector will be
\begin{pmatrix}-6\\6\end{pmatrix}
Question 4
Rotate shape A 180^\circ about the point (0,2). Label this new shape B.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
To start, we need to find our centre of rotation, (0,2).
Now, using tracing paper we would trace the shape onto the tracing paper and place our pencil onto the centre of rotation. Then, twist the paper one half-turn (the nice thing about rotating 180^\circ it doesn’t matter which way we actually rotate!) and where the traced shape has moved is the result of your rotation.
Question 5
Enlarge the following shape by a scale factor of 4 about the point (2,1).
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
To start, we need to find our point of enlargement, (2,1).
We now need to draw a line from our point to each corner of the shape, I will start with A.
We can see that this line is 2 high, so if we want to enlarge this shape by 4, we’ll have to multiply this line’s height by 2, 2\times4=8.
Now, if we do the same with D, we can see that we go 3 across and 2 up:
So, if we enlarge by 4, we’ll have to go 3\times4=12 across and 2\times4=8 up.
So, if we enlarge by 4, we’ll have to go 3\times4=12 across and 2\times4=8 up.
To finish, we just need to connect our new points in the same way as the original points.
Question 6
Enlarge the following shape by a scale factor of 2.5 from the origin.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
To start, we need to find our point of enlargement. The origin is (0,0).
We now need to draw a line from our point to each corner of the shape, I will start with A.
If we break this up, we can see that we go right 4 and up 2.
So, if we enlarge by 2.5, we’ll have to go 4\times2.5=10 right and 2\times2.5=5 up.
Repeating the process for B and C will give us a diagram like this:
To finish, we just need to connect our new points in the same way as the original points.
