State Testing Prep: Chapter 10

Which sequence of transformations is used to transform the original image to the final image? Original: ABCD Final: A" B" C"D"

• Reflect over the x-axis and then rotate clockwise 90 around the origin.

• Rotate counterclockwise 90 around the origin and then translate 8 units left.

• Reflect over the y-axis and then rotate counterclockwise 90 around the origin.

• Rotate clockwise 90 around the origin and then translate 8 units left.

Two trapezoids are shown on the coordinate grid. Which sequence of transformations shows that the two trapezoids are congruent?

• Translate Trapezoid 1 to the right 6 units, then translate the resulting down 2 units.

• Reflect Trapezoid 1 across the x-axis, then reflect the resulting figure across the y-axis.

• Translate Trapezoid 1 to the right 6 units, then reflect the resulting figure across the x-axis.

• Translate Trapezoid 1 down 2 units, then reflect the resulting figure across the y-axis.

If RQ is rotated 180 degrees about the origin and then translated 1 unit right and 1 unit to down, what are the endpoints of the resulting image?

• R' (1, -1) Q' (-1, 2)

• R' (2, -2) Q' (0, 1)

• R' (0, 0) Q' (2, -3)

• R' (0, -2) Q' (-3, 1)

If QR is rotated 270 degrees counterclockwise about the origin and then translated 2 units down and 3 units to the left, what are the endpoints of the resulting image?

• Q' (-2, -3) R'(-4, 0)

• Q' (-1, -4) R'(-3, -1)

• Q' (1, 1) R'(-2, 1)

• Q' (1, -1) R'(-1, 2)

If QR is rotated 90 degrees clockwise about the origin and then translated 2 units to the left and 3 units up, what are the endpoints of the resulting image?

• Q'(1, 2) R'(-4, 4)

• Q'(-1, -3) R'(1, 2)

• Q'(-3, 1) R'(2, -1)

• Q'(-5, 4) R'(0, 2)

Triangle EGF will be rotated 90° counterclockwise around the origin and will then be reflected across the y-axis, producing an image triangle. Which additional transformation will map the image triangle back onto the original triangle?

• Rotation 270° counterclockwise around the origin

• Reflection across the line y = -x

• Rotation 180° counterclockwise around the origin

• Reflection across the line y = x

Plot A(1,1) B(3,1) C(2,4). Rotate it 90° clockwise, then reflect it over the y-axis. What are the new coordinates of A'B'C'?

• A' (-1, -1) B' (-1, -3) C' (-4, -2)

• A' (-1, 1) B' (-1, 3) C' (-4, 2)

• A' (1, -1) B' (1, -3) C' (4, -2)

• A' (-1, -1) B' (-3, -1) C' (-2, -4 )

Plot A(4,1) B(5,4) C(1,2). Reflect it over the x-axis, then translate it 3 units left. What are the coordinates of A'B'C'?

• A' (-1, -1) B' (-2, -4) C' (2, -2)

• A' (4, -4) B' (5, -7) C' (1, -5)

• A' (-7, 1) B' (-8, 4) C' (-4, 2)

• A' (1, -1) B' (2, -4) C' (-2, -2)

A point in Quadrant II of the coordinate plane is reflected over the y-axis and translated right. Which quadrant contains the transformed point?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Polygon KLMNP is reflected across the line x = −1. What are the coordinates of the image of vertex P after this reflection?

Answer explanation

Construct the vertical line x = -1, then flip the point P over that and name the new coordinates of P' .