問 1
1 点Which of the following matrices represents a linear enlargement about the origin with a scale factor of 3?
Pearson Edexcel International A Level · Further Mathematics (YFM01)
Transformations using matrices：練習問題
その場で採点される選択問題 5 問と、解説つきの記述問題 4 問。すべて「Transformations using matrices」からの出題です。
9 問20 点無料・登録不要
問 2
1 点The matrix \( T = \begin{pmatrix} 2 & k \\ -1 & 4 \end{pmatrix} \) transforms a triangle with area 5 units\(^2\) to a triangle with area 45 units\(^2\). Given that \( k \) is a positive constant, find the value of \( k \).
問 3
1 点A linear transformation \(T_1\) is a rotation through \(90^\circ\) clockwise about the origin. A second linear transformation \(T_2\) is a reflection in the line \(y = -x\). Which of the following geometric transformations is equivalent to the combined transformation of \(T_1\) followed by \(T_2\)?
問 4
1 点A linear transformation \( S \) consists of a reflection in the \( x \)-axis followed by a rotation of \( 90^\circ \) anticlockwise about the origin. Find the single matrix that represents \( S \).
問 5
1 点A linear transformation \( M \) maps the unit square with vertices \( (0,0), (1,0), (0,1), \) and \( (1,1) \) to a shape with vertices \( (0,0), (2,3), (-1,4), \) and \( (1,7) \) respectively. Find the matrix \( M \).
問 6
2 点State the geometric transformation represented by the matrix \( \mathbf{M} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \).
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問 7
3 点A triangle \( T \) has an area of \( 12 \text{ cm}^2 \). Find the area of the image of \( T \) after it has been transformed by the matrix \( \mathbf{A} = \begin{pmatrix} 3 & 1 \\ 2 & 4 \end{pmatrix} \).
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問 8
5 点The matrix \( \mathbf{P} \) represents a reflection in the line \( y = x \) and the matrix \( \mathbf{Q} \) represents a rotation of \( 90^\circ \) anticlockwise about the origin. Find the single matrix that represents the transformation \( \mathbf{P} \) followed by \( \mathbf{Q} \).
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問 9
5 点The linear transformation \(T\) is represented by the matrix \( {A} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \), and the linear transformation \(U\) is represented by the matrix \( {B} = \begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix} \).
(a) Describe geometrically the transformations represented by \( {A} \) and \( {B} \).
(b) Find the matrix \( {C} \) that represents the transformation \(T\) followed by \(U\).
(c) A triangle with area 5 square units is transformed by \( {C} \). Find the area of the image triangle.
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