Let me work through each matrix transformation carefully to match them with the correct descriptions.
Matrix a: $\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}$
This is a diagonal matrix with both diagonal elements equal to 3. This represents an enlargement (scaling) by a factor of 3 from the origin. Every point gets multiplied by 3 in both x and y directions.
Matrix b: $\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}$
This matrix negates both x and y coordinates. This is equivalent to a rotation of 180° about the origin, or it can also be seen as a reflection through the origin.
Matrix c: $\begin{pmatrix} 0 & -1 \\ -1 & 0 \end{pmatrix}$
Let me check what this does:
- Point (x, y) becomes (-y, -x)
- This is a reflection at the line y = -x
Matrix d: $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$
This negates only the x-coordinate while keeping y the same. This is a reflection at the y-axis.
Matrix e: $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$
This keeps x the same but negates y. This is a reflection at the x-axis.
Matrix f: $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$
This is the identity matrix - it leaves all points unchanged.
Matrix g: $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
Let me check: Point (x, y) becomes (y, x). This swaps x and y coordinates, which is a reflection at the line y = x.
Matrix h: $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$
Point (x, y) becomes (-y, x). Let me verify this is a 90° anticlockwise rotation:
- (1, 0) → (0, 1) ✓
- (0, 1) → (-1, 0) ✓
Yes, this is a rotation of 90° anticlockwise about the origin.
Matrix i: $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$
Point (x, y) becomes (y, -x). Let me verify this is a 270° anticlockwise rotation (or 90° clockwise):
- (1, 0) → (0, -1) ✓
- (0, 1) → (1, 0) ✓
Yes, this is a rotation of 270° anticlockwise about the origin.
Now let me match each letter with the correct description:
a → Enlargement with scale factor 3 at origin
b → Rotation 180° at origin
c → Reflection at y = -x
d → Reflection at y axis
e → Reflection at x axis
f → Identity matrix
g → Reflection at y = x
h → Rotation about origin at 90° anticlockwise directions
i → Rotation at origin 270° anticlockwise direction
Final Answer:
a - Enlargement with scale factor 3 at origin
b - Rotation 180° at origin
c - Reflection at y = -x
d - Reflection at y axis
e - Reflection at x axis
f - Identity matrix
g - Reflection at y = x
h - Rotation about origin at 90° anticlockwise directions
i - Rotation at origin 270° anticlockwise direction
Parent Tip: Review the logic above to help your child master the concept of transformations with matrices worksheet.
