Describe the transformation of a triangle (1, 1), (2, 3), (3, 1) reflected over the line y = -x.

Describe the transformation of a triangle (1, 1), (2, 3), (3, 1) reflected over the line y = -x.

• A. (-1, -1), (-3, -2), (-1, -3)
• B. (1, 1), (2, 3), (3, 1)
• C. (1, -1), (3, -2), (1, -3)
• D. (-2, -2), (-1, -3), (-3, -1)

Answer: (A)

To understand the transformation of the triangle given by the points (1, 1), (2, 3), and (3, 1) reflected over the line y = -x, we need to apply the rules of reflection for this specific line. When a point (x, y) is reflected over the line y = -x, the new coordinates become (-y, -x). Therefore, we will transform each vertex of the triangle individually: 1. For the point (1, 1): - Reflecting over y = -x gives us (-1, -1). 2. For the point (2, 3): - Reflecting over y = -x gives us (-3, -2). 3. For the point (3, 1): - Reflecting over y = -x gives us (-1, -3). Thus, the new vertices of the triangle after reflection over the line y = -x are (-1, -1), (-3, -2), and (-1, -3). This matches perfectly with the first option. The other choices do not align with the calculated reflections, as they either repeat the original points or contain incorrect transformations based on the reflection

To understand the transformation of the triangle given by the points (1, 1), (2, 3), and (3, 1) reflected over the line y = -x, we need to apply the rules of reflection for this specific line.

When a point (x, y) is reflected over the line y = -x, the new coordinates become (-y, -x). Therefore, we will transform each vertex of the triangle individually:

1. For the point (1, 1):

• Reflecting over y = -x gives us (-1, -1).

2. For the point (2, 3):

• Reflecting over y = -x gives us (-3, -2).

3. For the point (3, 1):

• Reflecting over y = -x gives us (-1, -3).

Thus, the new vertices of the triangle after reflection over the line y = -x are (-1, -1), (-3, -2), and (-1, -3).

This matches perfectly with the first option. The other choices do not align with the calculated reflections, as they either repeat the original points or contain incorrect transformations based on the reflection