Question

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?
1 point
Translation 3 units up and 2 units right
Translation 2 units up and 2 units left

Answer 1

To determine the transformation applied to the triangle, we can analyze the shift from the initial vertices to the final vertices.

Original vertices:
- A(2, 3)
- B(3, 5)
- C(5, 3)

Transformed vertices:
- A'(4, 6)
- B'(5, 8)
- C'(7, 6)

Now, let's calculate the translation for one of the points. We'll use point A and its transformation to A':

1. A(2, 3) is transformed to A'(4, 6).
- Change in x: 4 - 2 = 2
- Change in y: 6 - 3 = 3

This indicates that all points have been translated 2 units to the right (increase in x) and 3 units up (increase in y).

Now, let's verify this translation with one of the other points, B(3, 5) to B'(5, 8):

2. B(3, 5) is transformed to B'(5, 8).
- Change in x: 5 - 3 = 2
- Change in y: 8 - 5 = 3

For point C(5, 3) to C'(7, 6):

3. C(5, 3) is transformed to C'(7, 6).
- Change in x: 7 - 5 = 2
- Change in y: 6 - 3 = 3

Since all points have been translated consistently, we can conclude that the transformation applied is a translation of 2 units right (for x) and 3 units up (for y).

To answer the question, the transformation is **Translation 3 units up and 2 units right**.