Question

Two four-sided polygons are plotted on a coordinate plane. One polygon is at A(15, 10), B(15, 20), C(20, 15), and D(20, 5). Another polygon is at G(-15, -10), H(-5, -10), I(-10, -5), and J(-20, -5). The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is ________ followed by ________?

1) reflection over the x-axis, translation 10 units to the right
2) reflection over the y-axis, translation 10 units to the left
3) reflection over the x-axis, translation 10 units to the left
4) reflection over the y-axis, translation 10 units to the right

Answer 1

The sequence of transformations that can be performed is reflection over the x-axis followed by translation 10 units to the left.

Step-by-step explanation:

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is:

1. Reflection over the x-axis: This will change the y-coordinates of the vertices to their opposites (positive becomes negative and vice versa).
2. Translation 10 units to the left: This will change the x-coordinates of the vertices by subtracting 10.

By performing these two transformations on quadrilateral ABCD, it will become congruent to quadrilateral GHIJ.