Question

Describe the series of transformations that have occurred to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent. (1 point)

Rotation, then translation

translation, then rotation

reflection, then translation

rotation, then reflection

Answer 1

To determine the series of transformations to move a triangle in Quadrant IV to a triangle in Quadrant II and show that the triangles are congruent, we need to analyze the positions of the triangles in the Cartesian coordinate system.

1. **Quadrant IV**: In this quadrant, both x-coordinates are positive and y-coordinates are negative.
2. **Quadrant II**: In this quadrant, x-coordinates are negative and y-coordinates are positive.

Given that congruent triangles can be moved from one position to another through a series of transformations such as translations, rotations, reflections, or a combination thereof, we can consider the necessary changes in the coordinates:

- To move from Quadrant IV to Quadrant II, the triangle must change positions such that:
- The x-coordinates change from positive to negative, suggesting a reflection across the y-axis.
- The y-coordinates change from negative to positive, indicating that points must be moved upward.

The most efficient way to achieve this is:

1. **Reflection** across the y-axis: This will turn the triangle in Quadrant IV into a triangle that is still in Quadrant III (thus still below the x-axis but also now on the negative side of the x-axis).
2. **Translation** upward: This will move the triangle from Quadrant III to Quadrant II, making its y-coordinates positive.

Thus, the series of transformations that occurred to move the triangle in Quadrant IV to the triangle in Quadrant II is:

**Reflection, then translation.**