Question

Circle Q was transformed to create circle Q'. Which rule best describes the transformation that was applied to circle Q to create circle Q?

a) (x,y) → (y,x)
b) (x,y) → (x-6, y-8)
c) (x,y) → (-x, -y)
d) (x,y) → (x, -y)

Answer 1

Without additional information on the positioning of circle Q' relative to circle Q, it's not possible to identify which transformation (reflection, translation, or rotation) was applied. Option (b) represents a translation, (c) a rotation, and (d) a reflection over the x-axis.

Step-by-step explanation:

To determine which transformation rule was applied to circle Q to create circle Q', we should look at the characteristics of each potential transformation:

• (a) (x,y) → (y,x) represents a reflection over the line y = x.
• (b) (x,y) → (x-6, y-8) represents a translation, moving the circle 6 units left and 8 units down.
• (c) (x,y) → (-x, -y) represents a rotation of 180 degrees around the origin.
• (d) (x,y) → (x, -y) represents a reflection over the x-axis.

Without additional information about how circle Q' is positioned in relation to circle Q, we cannot definitively determine which transformation from the options a, b, c, or d has been applied. However, if circle Q' maintains its size and shape but is in a different position, options b, c, and d are more likely than option a, which would also change the orientation of any asymmetrical features on the circle.