Answer:
Part A: Figure 1 → Figure 4
Rigid Transformation
Equivalent to a reflection about the origin, or a rotation of 180° clockwise or anticlockwise about the origin which are types of rigid transformation
Part B: Figure 2 → Figure 5
Similarity transformation
Figure 5 is Figure 2 dilated by a scale factor of 1/2, which is a form of a similarity transformation
Explanation:
Part A: Figure 1 → Figure 4
The coordinates of the vertices of the preimage are;
(5, 10), (2, 4), (9, 2)
The coordinates of the vertices of the image are;
(-9, -2), (-2, -4), (-5, -10)
Which is equivalent to a reflection about the origin, or a rotation of 180° clockwise or anticlockwise about the origin
Part B: Figure 2 → Figure 5
The coordinate points of figure 2 are;
(-9, 2), (-5, 10), and (-2, 4)
The coordinate points of figure 5 are;
(1, 2), (2.5, -1), and (4.5, 3)
The lengths of the sides of figure 2 are;
√((10 - 2)² + ((-5) - (-9))²) = 4·√5
√((10 - 4)² + ((-5) - (-2))²) = 3·√5
√((2 - 4)² + ((-9) - (-2))²) = √53
The lengths of the sides of figure 5 are;
√(((-1) - 2)² + (2.5 - 1)²) = (3·√5)/2
√((4.5 - 2.5)² + (3 - (-1))²) = 2·√5
√((4.5 - 1)² + (3 - 2)²) = (√53)/2
Therefore. Figure 5 is Figure 2 dilated by a scale factor of 1/2
Therefore, given that the sides of Figure 2 and Figure 5 are rotated by 180°
We have;
Figure 5 is obtained as follows;
1) The rotation of figure 2 by 180°, clockwise or anticlockwise about the origin to get;
(-9, 2), (-5, 10), and (-2, 4) → (9, -2), (5, -10), and (2, -4)
2) The image is translated left by 1 blocks and up by 6 blocks as follows;
(9, -2), (5, -10), and (2, -4) → (8, 4), (4, -4), and (1, 2)
3) The image is then dilated by a scale factor of 1/2 with a center of dilation of (1, 2) to get;
Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).