Answer:
C' = (15, 7)
Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.
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 (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.
Given:
If ΔABC is dilated by a scale factor of 3, with the origin as the center of dilation, B' = (3, 12). If the triangle is then translated 1 unit up, B' = (3, 13), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
- Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation.
- Translation of 1 unit up.
Mapping Rule: (x, y) → (3x, 3y + 1)
Therefore, the coordinates of point C' are:
⇒ C' = (3(5), 3(2) + 1) = (15, 7)