11.05 Composing transformations
For each of the following, state the two types of transformations that would be needed to get from Flag A to Flag B:
State the two types of transformations that would be needed to get from:
Flag A to Flag B.
Flag A to Flag C.
When the original shape is rotated 90 \degree anti-clockwise about point O and then translated 3 units up, which of the shapes shown is the new shape?
Triangle M is to be rotated 90 \degree clockwise about point O, then translated 3 units left.
Which triangle corresponds to the result of this transformation?
Identify the correct square when the original is rotated 90 \degree anticlockwise about point Q, then reflected across the line PR, and then translated 4 units to the left.
Square ABCD is reflected across a vertical line and then rotated 90 \degree clockwise about its centre. This process is repeated with each resulting square. The result of the first set of reflection and rotation is shown:
After 13 repetitions of this process, write down the vertices, clockwise from the top left corner.
Point A on the plane is to undergo two successive transformations:
Plot point A', which is the result when point A is translated 4 units left.
Plot point A'', which is the result when point A' is rotated 90 \degree clockwise about the origin.
Point A on the plane is to undergo two successive transformations:
Plot point A', which is the result when point A is translated 5 units downwards.
Plot point A'', which is the result when point A' is rotated 90 \degree anticlockwise about the origin.
Point A on the plane is to undergo two successive transformations:
Plot point A', which is the result when point A is translated 3 units right and 5 units down.
Plot point A'', which is the result when point A' is rotated 90 \degree anticlockwise about the origin.
For the point on the plane, plot the point that will result from a translation of 5 units left followed by a rotation of 90 \degree clockwise about the origin.
For the point on the plane, plot the point that will result from a translation of 2 units downwards followed by a rotation of 90 \degree anticlockwise about the origin.
For the point on the plane, plot the point that will result from a translation of 3 units left and 4 units down, followed by a rotation of 90 \degree anticlockwise about the origin.
Consider the two points, A and B on the plane:
Plot the points that would result when A and B are first rotated 180 \degree about the origin, and then reflected across the x-axis.
Consider the two points, A and B on the plane:
Plot the points that would result when A and B are rotated 180 \degree about the origin and reflected across the y-axis.
What single transformation would give the same result?
Plot the triangle that will result when the given triangle is reflected across the x-axis and translated 3 units to the left.
Plot the triangle that will result when the given triangle is reflected across the y-axis and translated 2 units up.
Plot the triangle that will result when the given triangle is reflected across the y-axis, and translated 3 units left and 2 units down.
Plot the triangle that will result when the given triangle is reflected across the x-axis, and translated 3 unit right and 2 units up.
Consider the triangle ABC:
Plot triangle A'B'C', the result of reflecting triangle ABC across the line y = x.
Suppose triangle A'B'C' is reflected across the y-axis to form triangle A''B''C''. What single transformation would transform triangle ABC straight to triangle A''B''C''?
Point A is marked on the number plane:
If point A is translated 4 units down to make point B, what are the coordinates of point B?
Across what line could point A be reflected across so that it makes point \\ B?
Describe the sequence of transformations required to get from quadrilateral ABCD to quadrilateral A''B''C''D''. Use quadrilateral A'B'C'D' as a guide.
Describe the sequence of transformations required to get from quadrilateral ABCD to quadrilateral A''B''C''D''.
Describe the sequence of transformations required to get from triangle ABC to triangle A''B''C''. Use triangle A'B'C' as a guide.
Describe the sequence of transformations required to get from triangle ABC to triangle A''B''C''.
Point A \left( - 10 , 6\right) is rotated 90 \degree clockwise about the origin to form point B.
Write down the the coordinates of point B.
Point B is then translated to the left so that it lies on the same vertical line as point A. How many units to the left is point B translated?
For the point on the plane \left( - 6 , 9\right), write down the coordinates of the point that will result from a translation of 4 units left followed by a rotation of 90 \degree clockwise about the origin.
For the point on the plane \left( - 2 , - 1 \right), write down the coordinates of the point that will result from a translation of 2 units up followed by a rotation of 90 \degree clockwise about the origin.
For each of the following points, write down the coordinates of the point that will result from a translation of 2 units right followed by a rotation of 90 \degree anticlockwise about the origin:
\left(4, 5\right)
\left( - 7 , - 6 \right)
For the point on the plane \left(1, 4\right), write down the coordinates of the point that will result from a translation of 4 units left and 3 units down, followed by a rotation of 90 \degree clockwise about the origin.
For the point on the plane \left(3, - 6 \right), write down the coordinates of the point that will result from a translation of 4 units right and 5 units down, followed by a rotation of 90 \degree anticlockwise about the origin.
The point A \left(6, - 1 \right)is first rotated 180 \degree about the origin, and then it is reflected across the \\ x-axis to make point A'.
Write down the coordinates ofA'.
Describe a single transformation onA that will produce the same result as part (a).
Consider the points: A \left( - 4 , - 4 \right) and B \left(8, 4\right)
Write down the coordinates of the points that would result when the original points are rotated 180 \degree about the origin and reflected across the x-axis.
Describe a single transformation on A and B that will produce the same result as part (a).
Consider the points: A \left( - 1 , 2\right) and B \left( - 7 , - 3 \right)
Write down the coordinates of the points that would result when the original points are rotated 180 \degree about the origin and reflected across the y-axis.
Describe a single transformation on A and B that will produce the same result as part (a).
Points A \left( - 4 , - 2 \right), B \left( - 1 , - 9 \right) and C \left( - 10 , - 6 \right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the x-axis and translating it 4 units left.
Points A \left(5, - 9 \right), B \left( - 1 , - 4 \right) and C \left(2, 5\right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the x-axis and translating it 5 units down.
Points A \left(2, - 8 \right), B \left(8, 5\right) and C \left(7, 6\right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the y-axis and translating it 4 units right.
Points A \left( - 9 , - 1 \right), B \left(10, 5\right) and C \left(10, 1\right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the y-axis and translating it 4 units down.
Points A \left(6, 7\right), B \left( - 3 , 8\right) and C \left( - 3 , 10\right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the x-axis, and translating it 5 units left and 4 units down.
Points A \left(4, - 4 \right), B \left(10, 3\right) and C \left(9, 9\right) are the vertices of a triangle. Write down the coordinates A', B' and C' that result from reflecting the triangle across the y-axis, and translating it 3 units right and 5 units down.
For any point \left(x, y\right) on the plane, write down the coordinates of the point after a rotation of 180 \degree anticlockwise about the origin.
What two reflections result in the same transformation as rotating a point 180 \degree anticlockwise about the origin?
For any point \left(a, b\right) on the plane, state the coordinates of the point after a reflection across the x-axis.
Consider the point A \left( - 9 , 0\right).
If point A is rotated 90 \degree clockwise about the origin to produce point B, find the coordinates of point B.
Describe the two translations that can be used to move point A to point B.
Consider the point A \left( - 5 , 6\right).
If point A is reflected across the y-axis to produce point B, and point B is then reflected across the x-axis to produce point C, find the coordinates of point C.
Describe a single transformation to move point A to point C.