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. The first transformation is a reflection over the y-axis. This means that all the points in the original triangle are reflected across the y-axis to create a new triangle. This new triangle will now be located in quadrant I instead of quadrant IV.
2. The second transformation is a translation. The entire triangle is shifted to a new position in the coordinate plane. This translation can be done horizontally or vertically, depending on how the new triangle should be positioned relative to the original triangle. In this case, let's assume the new triangle is shifted horizontally by a distance of x units.
3. The third transformation is a reflection over the x-axis. This means that all the points in the translated triangle are reflected across the x-axis to create a final triangle in quadrant II. This reflection allows us to position the new triangle properly in quadrant II.
Overall, the series of transformations consists of a reflection over the y-axis, followed by a translation, and finally a reflection over the x-axis. These transformations move the triangle in quadrant IV to the triangle in quadrant II and ensure that the two triangles are congruent.