Question

The coordinates of the vertices of triangle ABC are A(3,6), B(6,3), and C(9,9). If triangle ABC is dilated by (x,y) - (1/3x, 1/3y) to create triangle A'B'C', which set of coordinates represents the vertices of triangle A'B'C'?

A. A'(2,5), B'(2,1), C'(3,3)
B. A'(9.18, 18), B'(18, 9.18), C'(27.27, 27.27)
C. A'(12, 2.1), B'(2.1, 12), C'(3, 3)
D. Not here

Answer 1

The dilated triangle A'B'C' vertices are A'(1, 2), B'(2, 1), and C'(3, 3), which do not match any of the options provided, so the correct answer is D. Not here.

Step-by-step explanation:

The student has asked for the coordinates of the vertices of triangle A'B'C' after the dilation of triangle ABC with vertices A(3,6), B(6,3), and C(9,9) by a factor of (1/3) using the transformation (x,y) -> (1/3x, 1/3y). To find the coordinates of the dilated triangle A'B'C', each vertex of triangle ABC needs to be multiplied by 1/3.

1. For vertex A(3,6), the dilated coordinates A' would be (1/3 * 3, 1/3 * 6) = (1, 2).
2. For vertex B(6,3), the dilated coordinates B' would be (1/3 * 6, 1/3 * 3) = (2, 1).
3. For vertex C(9,9), the dilated coordinates C' would be (1/3 * 9, 1/3 * 9) = (3, 3).

Therefore, the vertices of triangle A'B'C' are A'(1, 2), B'(2, 1), and C'(3, 3). These coordinates do not match any of the options provided by the student, so the correct answer is D. Not here.