A triangle with vertices at (1,1), (4,1), and (1,3) is transformed to a triangle with vertices at (3,1), (6,1), and (3,3). Which transformation was applied?

Question

1 point
Translation 2 units to the right
Reflection over the y-axis
Translation 2 units up

Answer 1

To determine the transformation applied to the triangle with vertices at (1, 1), (4, 1), and (1, 3) to arrive at the new triangle with vertices at (3, 1), (6, 1), and (3, 3), we can analyze the changes in the coordinates of the vertices.

1. The original triangle has the following vertices:

   • A(1, 1)
   • B(4, 1)
   • C(1, 3)

2. The transformed triangle has these vertices:

   • A'(3, 1)
   • B'(6, 1)
   • C'(3, 3)

Now we can observe how each vertex changes:

• A(1, 1) to A'(3, 1): The x-coordinate increases by 2 (1 + 2 = 3), while the y-coordinate remains the same.
• B(4, 1) to B'(6, 1): The x-coordinate again increases by 2 (4 + 2 = 6), while the y-coordinate remains the same.
• C(1, 3) to C'(3, 3): The x-coordinate increases by 2 (1 + 2 = 3), while the y-coordinate remains the same.

Since all the points have their x-coordinates increased by 2 and their y-coordinates remain unchanged, we can conclude that the transformation applied is a translation 2 units to the right.

Therefore, the answer is:

Translation 2 units to the right.