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

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1 point
Translation 2 units to the right
Reflection over the y-axis
Rotation 90 degrees clockwise about the origin
Translation 2 units up

Answer 1

To determine the transformation applied to the triangle, we can look at the coordinates of the original triangle and the transformed triangle.

The original triangle has vertices at:

• A(1, 1)
• B(4, 1)
• C(1, 3)

The transformed triangle has vertices at:

• A'(3, 1)
• B'(6, 1)
• C'(3, 3)

Now let's analyze the changes for each vertex:

• For A(1, 1) to A'(3, 1):

  • The x-coordinate changes from 1 to 3 (which is a translation of 2 units to the right).
  • The y-coordinate remains the same.

• For B(4, 1) to B'(6, 1):

  • The x-coordinate changes from 4 to 6 (which is also a translation of 2 units to the right).
  • The y-coordinate remains the same.

• For C(1, 3) to C'(3, 3):

  • The x-coordinate changes from 1 to 3 (again, a translation of 2 units to the right).
  • The y-coordinate remains the same.

Since all the vertices of the original triangle have been translated 2 units to the right, the correct transformation is:

Translation 2 units to the right.