Question

Triangle ABC is dilated by a scale factor of 3. The vertices of ABC are A(1,5), B(2,3), and C(4,2). What are thevertices of Triangle A'B'C'?

A) A'(3,15), B'(6,9), C'(12,6).
B) A'(1,15), B'(2,9), C'(4,6).
C) A'(3,5), B'(6,3), C'(12,2).
D) A'(1/3, 5/3), B'(2/3,1), C'(4/3, 2/3).

Answer 1

To find the vertices of the dilated triangle A'B'C', you need to multiply the coordinates of each vertex of triangle ABC by the scale factor of 3. The vertices of triangle A'B'C' are A'(3, 15), B'(6, 9), and C'(12, 6).

Step-by-step explanation:

To find the vertices of the dilated triangle A'B'C', we need to multiply the coordinates of each vertex of triangle ABC by the scale factor of 3.

Starting with vertex A(1, 5), we multiply the x-coordinate by 3 to get the x-coordinate of A', which is 3, and we multiply the y-coordinate by 3 to get the y-coordinate of A', which is 15. So, A' is located at (3, 15).

Similarly, for vertex B(2, 3), we multiply the x-coordinate by 3 to get the x-coordinate of B', which is 6, and we multiply the y-coordinate by 3 to get the y-coordinate of B', which is 9. So, B' is located at (6, 9).

For vertex C(4, 2), we again multiply the x-coordinate by 3 to get the x-coordinate of C', which is 12, and we multiply the y-coordinate by 3 to get the y-coordinate of C', which is 6. So, C' is located at (12, 6).

Therefore, the vertices of triangle A'B'C' are A'(3, 15), B'(6, 9), and C'(12, 6). Thus, the correct answer is Option A) A'(3,15), B'(6,9), C'(12,6).