(a) Describe fully the single transformation that maps triangle \( A \) onto triangle \( B \).
(b) Draw the image of triangle \( A \) after
(i) a reflection in the line \( y = 1 \)
(ii) a translation by the vector \(\begin{pmatrix} 5 \\ -7 \end{pmatrix}\)
(iii) an enlargement, scale factor 2, centre (\(-4\), \(5\)).
(a) Rotation 90° anticlockwise about the point (2, 7)
Triangle A is rotated 90 degrees counter-clockwise around the center point (2,7) to match the position of triangle B.
(b)(i) Image at (-4, -1), (-3, -1), (-4, -4)
Each point of triangle A is reflected across the horizontal line y=1, flipping the triangle vertically while maintaining equal distances from the mirror line.
(b)(ii) Image at (2, -4), (1, -4), (1, -1)
Every point of triangle A is moved right 5 units and down 7 units according to the translation vector (5,-7).
(b)(iii) Image at (-4, 7), (-4, 1), (-2, 1)
Triangle A is enlarged by scale factor 2 from the center point (-4,5), doubling all distances from this point while maintaining the shape.
