Rotations and Dilations

Triangle ABC has vertices A(-4, 1), B(-2, 1), and C(-1, -2) on a coordinate grid. If ∆ABC is rotated 180° about the origin, what are the coordinates of A'B'C'?

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

Rotation Rules (clockwise):

90^o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90^⁰ rotation clockwise?

• (1, 3)

• (3, 1)

• (3, -1)

• (1, -3)

Rotation Rules (clockwise):

180^o rotation: (x, y)→(-x, -y)

What are the coordinates of C' after a rotation of 180° clockwise?

• (-3, -1)

• (3,1)

• (1,3)

• (-1, -3)

Rotation Rules (clockwise):

270^o rotation: (x, y)→(-y, x)

What are the coordinates of B' after a 270° clockwise?

• (4, 4)

• (4, -4)

• (-3, 4)

• (-4, 4)

If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be?

• (-5, 5)
• (-3, 5)
• (-5, 3)
• (-3, 3)

What is the angle of rotation for this counterclockwise rotation about the origin?

• 90°
• 180°
• 270°
• 360°

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

• (5,3)
• (20,12)
• (-20,-12)
• (-5,-3)

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor k = 2.

• (2,4.5)
• (-8,-18)
• (8,18)
• (9,4)

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)
• (6,0), (9,-3), (-6,-15)
• (2/3,0), (1,-1/3), (-2/3,-5/3)
• (-1,-3), (0,-4), (-5,-8)

Does the image show a Dilation?

• Yes
• No