Find the coordinates of the figure after the transformations. Reflect the trapezoid in the x-axis. Then translate the trapezoid 2 units left and 3 units up. (-2,1),(2,1),(4,-2),(-2,-2)

If point (x , y) reflected across the x-axis , then its image is (x , -y) , the rule of reflection is rx-axis (x , y) → (x , -y)
If point (x , y) reflected across the y-axis , then its image is (-x , y) , the rule of reflection is ry-axis (x , y) → (-x , y)
If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)

∵ The vertices of the trapezoid are (-2 , 1) , (2 , 1) , (4 , -2) , (-2 , -2)

∵ The trapezoid is reflected in the x-axis

- That means change the sign of each y-coordinate of its vertices

∴ Their images are (-2 , -1) , (2 , -1) , (4 , 2) , (-2 , 2)

∵ The trapezoid then is translated 2 units left

- That means subtract 2 from each x-coordinate of its new vertices

∵ (-2 - 2 , -1) , (2 - 2 , -1) , (4 - 2 , 2) , (-2 - 2 , 2)

∴ Their images are (-4 , -1) , (0 , -1) , (2 , 2) , (-4 , 2)

∵ The trapezoid then is translated 3 units up

- That means add 3 to each y-coordinate of its new vertices

∵ (-4 , -1 + 3) , (0 , -1 + 3) , (2 , 2 + 3) , (-4 , 2 + 3)

∴ Their images are (-4 , 2) , (0 , 2) , (2 , 5) , (-4 , 5)

The coordinates of the trapezoid after the transformations are:

(-4 , 2) , (0 , 2) , (2 , 5) , (-4 , 5)

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