Final answer:
To prove that quadrilateral ABCD is congruent to GHIJ, a reflection followed by a translation is required. The reflection is across the origin, and the translation is moving the figure 10 units up and 10 units to the right.
Step-by-step explanation:
To answer the question of how to perform a sequence of transformations on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ, we first need to observe the positions of the points in a coordinate plane. The vertices of quadrilateral ABCD are at A (15, 10), B (15, 20), C (20, 15), and D (20, 5), and the vertices of quadrilateral GHIJ are at G (-15, -10), H (-5, -10), I (-10, -5), and J (-20, -5).
Considering these positions, we can see that quadrilateral ABCD is located in the first quadrant, while quadrilateral GHIJ is in the third quadrant. To map one onto the other, we need two transformations: a reflection followed by a translation.
Reflection: Reflect quadrilateral ABCD across the origin to map it to the third quadrant. This reflection changes the sign of both the x- and y-coordinates, thus the image of point A (15, 10) would become A' (-15, -10), and similarly for the other points. After reflection, the new positions will be A' (-15, -10), B’ (-15, -20), C' (-20, -15), and D' (-20, -5).
Translation: Perform a translation to shift the reflected quadrilateral so that it coincides with GHIJ. The translation needed would be 10 units up and 10 units to the right. This would map A' to G, B’ to H, C' to I, and D' to J.
Therefore, the sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a reflection across the origin followed by a translation 10 units up and 10 units to the right.