Question

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Answer 1

To reflect the trapezoid in the x-axis, you need to change the sign of the y-coordinates while keeping the x-coordinates the same:

Original Points:
X = (-2, 1)
W = (-2, -2)
Y = (2, 1)
Z = (4, -2)

After reflecting in the x-axis:

X' = (-2, -1) (x stays the same, but y becomes -1)
W' = (-2, 2) (x stays the same, but y becomes 2)
Y' = (2, -1) (x stays the same, but y becomes -1)
Z' = (4, 2) (x stays the same, but y becomes 2)

Now, to translate the trapezoid 2 units left and 3 units up, you need to subtract 2 from the x-coordinates and add 3 to the y-coordinates:

Translated Points:

X'' = (-2 - 2, -1 + 3) = (-4, 2)
W'' = (-2 - 2, 2 + 3) = (-4, 5)
Y'' = (2 - 2, -1 + 3) = (0, 2)
Z'' = (4 - 2, 2 + 3) = (2, 5)

So, the coordinates of the final image after reflecting in the x-axis and then translating 2 units left and 3 units up are:

X'' = (-4, 2)
W'' = (-4, 5)
Y'' = (0, 2)
Z'' = (2, 5)

Answer 2

So, after applying the reflection and translation, the new positions of the points are:

W'(-4, 5)

X'(-4, 2)

Y'(0, 2)

Z'(2, 5)

These new points define the vertices of the trapezoid after the specified transformations.

Explanation:

To reflect the trapezoid across the x-axis and then translate it 2 units left and 3 units up, you can perform the following transformations on each of the four points (W, X, Y, Z):

Reflect across the x-axis: For each point (x, y), the reflected point will be (x, -y).

Translate 2 units left and 3 units up: For each point (x, y), the translated point will be (x - 2, y + 3).

Let's apply these transformations to each of the four points:

Point W(-2, -2):

Reflecting across the x-axis: (-2, 2)

Translating 2 units left and 3 units up: (-4, 5)

Point X(-2, 1):

Reflecting across the x-axis: (-2, -1)

Translating 2 units left and 3 units up: (-4, 2)

Item Y(2, 1):

Reflecting across the x-axis: (2, -1)

Translating 2 units left and 3 units up: (0, 2)

Point Z(4, -2):

Reflecting across the x-axis: (4, 2)

Translating 2 units left and 3 units up: (2, 5)

So, after applying the reflection and translation, the new positions of the points are:

W'(-4, 5)

X'(-4, 2)

Y'(0, 2)

Z'(2, 5)

These new points define the vertices of the trapezoid after the specified transformations.