Question

List the coordinates of the vertices of trapezoid ABCD after it has been rotated 90° counterclockwise about the origin and then reflected over the x-axis. A(−5,−3)B(−4,0)C(−2,0)D(0,−3)

Answer 1

The required coordinates are;

A''(-3, -5), B''(0, -4), C''(0, -2), and D''(-3, 0)

Explanation:

The given coordinates of the trapezoid ABCD are;

A(-5, -3) B(-4, 0), C(-2, 0) and D(0, -3)

Therefore, we have;

For a rotation 90° counterclockwise, we have for a given coordinates of the preimage (x, y) after a rotation 90° counterclockwise, the image will be located at (y, -x)

Therefore, for the points of the trapezoid, we have;

Preimage A(-5, -3) rotated 90° counterclockwise gives image A'(-3, 5)

Preimage B(-4, 0) rotated 90° counterclockwise gives image B'(0, 4)

Preimage C(-2, 0) rotated 90° counterclockwise gives image C'(0, 2)

Preimage D(0, -3) rotated 90° counterclockwise gives image D'(-3, 0)

For a reflection across the x-axis gives the transformation, preimage location (x. y), image location after reflection (x, -y)

Therefore, we have;

For the point A'(-3, 5), reflection across the x-axis gives A''(-3, -5)

For B'(0, 4), reflection across the x-axis gives B''(0, -4)

For C'(0, 2), reflection across the x-axis gives C''(0, -2)

For D(-3, 0), reflection across the x-axis gives D''(-3, 0)

Therefore, the required coordinates are;

A''(-3, -5), B''(0, -4), C''(0, -2), and D''(-3, 0).