8th grade Ch 6 L3

Triangle XYZ has vertices X(3, -1), Y(5, -4), and Z(1, -5). Graph △XYZ and its image after a 270° counterclockwise rotation about vertex X. Then give the coordinates of the vertices for △X'Y'Z'.

• X'(3, -1), Y'(0, -3), Z'(-1, 1)

• X'(3, -1), Y'(6, 1), Z'(7, -3)

• X'(3, -1), Y'(1, 2), Z'(5, 3)

• X'(3, -1), Y'(0, -5), Z'(1, -3)

Triangle XYZ has vertices X(3, -1), Y(5, -4), and Z(1, -5). Graph △XYZ and its image after a 180° clockwise rotation about the origin. Then give the coordinates of the vertices for △X'Y'Z'.

• X'(-3, 1), Y'(-5, 4), Z'(-1, 5)

• X'(-3, -1), Y'(-5, -4), Z'(-1, -5)

• X'(3, 1), Y'(5, 4), Z'(1, 5)

• X'(1, -3), Y'(4, -5), Z'(5, -1)

The difference between rotating a figure about a given point that is a vertex and rotating the same figure about the origin if the rotation is less than 360° is:

• The resulting positions of the figure will be different unless the vertex is at the origin.

• There is no difference; the figure ends up in the same position.

• The figure will always overlap itself after rotation.

• Rotating about a vertex always results in a larger figure.

What are the coordinates of the vertices for triangle R’S’T’ after triangle RST with vertices R(–7, 8), S(–7, 2), and T(–2, 2) is rotated 180° clockwise about the origin?

• R’(7, –8), S’(7, –2), T’(2, –2)

• R’(–8, 7), S’(–2, 7), T’(–2, 2)

• R’(–7, –8), S’(–7, –2), T’(–2, –2)

• R’(8, –7), S’(2, –7), T’(2, –2)

What are the coordinates of the vertices of quadrilateral ABCD after a 90° clockwise rotation about vertex A(–3, –4)?

• A'(–3, –4), B'(0, –6), C'(1, –3), D'(–1, –1)

• A'(–3, –4), B'(–6, –2), C'(–5, 1), D'(–3, 3)

• A'(–3, –4), B'(–6, –2), C'(–5, 1), D'(–7, –1)

• A'(–3, –4), B'(–6, –2), C'(–7, –5), D'(–9, –7)

A partial hubcap is shown. The completed hubcap should have rotational symmetry of which angles?

• 90°, 180°, and 270°

• 45°, 90°, and 180°

• 60°, 120°, and 180°

• 30°, 60°, and 90°

The right isosceles triangle PQR has vertices P(3, 3), Q(3, 1), and R(x, y) and is rotated 90° counterclockwise about the origin. Find the missing vertex of the triangle. Then graph the triangle and its image.

• R(1, 3)

• R(5, 3)

• R(3, 5)

• R(1, 1)

Select the capital letters in VIRGINIA that produce the same letter after being rotated 180°.

• I and N

• V and A

• R and G

• V and I

Triangle ABC has vertices A(0, 4), B(0, -2), and C(2, 0). The triangle is reflected over the x-axis. Then the image is rotated 180° counterclockwise about the origin. What are the coordinates of the final image?

• A'(0, -4), B'(0, 2), C'(-2, 0)

• A'(0, 4), B'(0, -2), C'(2, 0)

• A'(0, -4), B'(0, 2), C'(2, 0)

• A'(0, 4), B'(0, -2), C'(-2, 0)

A triangle is rotated 90° clockwise about the origin. Then the image is rotated 270° clockwise about the origin. a. Complete the algebraic representation to explain the effect of the series of transformations performed.

• (x, y) → (y, -x) → (x, y)

• (x, y) → (-y, x) → (-x, -y)

• (x, y) → (-x, -y) → (y, -x)

• (x, y) → (y, x) → (-x, y)