Question

You may use your formula sheet if needed.

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?
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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 with vertices at (1,1), (4,1), and (1,3) to transform it to the triangle with vertices at (3,1), (6,1), and (3,3), we can analyze the changes in the coordinates of the vertices.

1. Original vertices:
- A(1,1)
- B(4,1)
- C(1,3)

2. Transformed vertices:
- A'(3,1)
- B'(6,1)
- C'(3,3)

Now, let's look at the changes for each vertex:

- For vertex A:
- (1,1) → (3,1)
- The x-coordinate increases by \(3 - 1 = 2\) (2 units to the right).

- For vertex B:
- (4,1) → (6,1)
- The x-coordinate again increases by \(6 - 4 = 2\) (2 units to the right).

- For vertex C:
- (1,3) → (3,3)
- The x-coordinate increases by \(3 - 1 = 2\) (2 units to the right).

Since all the vertices have their x-coordinates increased by 2 units, we conclude that the transformation applied is a translation 2 units to the right.

Therefore, the correct answer is: **Translation 2 units to the right**.