What is the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent?
To prove that the triangle in Quadrant IV is congruent to the triangle in Quadrant II, we need to perform a series of transformations. Here is the sequence of steps for moving the triangle:
1. Translation: Move the triangle from Quadrant IV to the origin (Quadrant I) by shifting all of its vertices the same distance to the left and up. This ensures that the vertices of the translated triangle have the same coordinates as the original vertices, but are now located in Quadrant I.
2. Reflection: Reflect the translated triangle over the x-axis. This means flipping the triangle upside down so that the new positions of the vertices are equidistant from the x-axis, but with opposite y-coordinates.
3. Translation: Move the reflected triangle back to Quadrant II by shifting all of its vertices the same distance to the right and up. This places the triangle in Quadrant II with the same shape and size as the original triangle in Quadrant IV.
By following this sequence of transformations, you can demonstrate that the triangle in Quadrant IV and the triangle in Quadrant II are congruent.