Answer:
C' = (10, 1)
Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units down.
Explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Given vertices of triangle ABC:
- A = (0, 0)
- B = (1, 4)
- C = (5, 2)
To maintain similarity but not maintain congruence, dilate triangle ABC (since dilation keeps the corresponding angles of both triangles the same).
Given vertex of triangle A'B'C':
If ΔABC is dilated by a scale factor of 2, with the origin as the center of dilation, B' = (2, 8). If the triangle is then translated 3 units down, B' = (2, 5), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
- Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation.
- Translation of 3 units down.
Mapping Rule: (x, y) → (2x, 2y - 3)
Therefore, the coordinates of point C' are:
⇒ C' = (2(5), 2(2) -3) = (10, 1)