A triangle with vertices at (2,3), (3,5), and (5,3) is transformed to a triangle with vertices at (4,6), (5,8), and (7,6). Which transformation was applied?

Question

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1 point
Translation 2 units right and 3 units up
Translation 2 units up and 2 units left
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin

Answer 1

To determine the transformation applied to the triangle, we can analyze the coordinates of the vertices.

Original triangle vertices are:

1. \( A(2,3) \)
2. \( B(3,5) \)
3. \( C(5,3) \)

Transformed triangle vertices are:

1. \( A'(4,6) \)
2. \( B'(5,8) \)
3. \( C'(7,6) \)

Step 1: Check for Translation

We can find the translation vector by comparing the coordinates of the corresponding points.

For \( A \) to \( A' \):

• The movement in the x-direction: \( 4 - 2 = 2 \)
• The movement in the y-direction: \( 6 - 3 = 3 \)

For \( B \) to \( B' \):

• The movement in the x-direction: \( 5 - 3 = 2 \)
• The movement in the y-direction: \( 8 - 5 = 3 \)

For \( C \) to \( C' \):

• The movement in the x-direction: \( 7 - 5 = 2 \)
• The movement in the y-direction: \( 6 - 3 = 3 \)

Since all points are translated by \( 2 \) units to the right (increasing x by 2) and \( 3 \) units up (increasing y by 3), the transformation is a translation.

Final Conclusion

The transformation applied is: Translation 2 units right and 3 units up.

So the correct answer is: Translation 2 units right and 3 units up.