Question

what type of transformation involves flipping a figure over a line of symmetry? a. dilation b. rotation c. translation d. reflection
triangle a has coordinates (-6,2), (-7,4), and (-3,4). what are the new coordinates of triangle b if the triangle has been rotated 90 degrees counterclockwise and then reflected over the x = 0 line? a. (-6,-2), (-7,-4), and (-3,-4) b. (6,-2), (7,-4), and (3,-4) c. (4,-3), (4,-7), and (2,-6) d. (-4,3), (-4,7), and (-2,6)

Explanation:

Step1: Define transformation types

Dilation changes size, rotation turns a figure, translation slides it, and reflection flips over a line. So for the first - question, reflection is the correct transformation for flipping over a line of symmetry.

Step2: Apply rotation rule

The rule for a 90 - degree counterclockwise rotation of a point $(x,y)$ is $(-y,x)$.
For point $(-6,2)$: After rotation, it becomes $(-2, - 6)$.
For point $(-7,4)$: After rotation, it becomes $(-4,-7)$.
For point $(-3,4)$: After rotation, it becomes $(-4,-3)$.

Step3: Apply reflection rule

The rule for reflecting a point $(x,y)$ over the line $x = 0$ (the y - axis) is $(-x,y)$.
For $(-2,-6)$: After reflection, it becomes $(2,-6)$.
For $(-4,-7)$: After reflection, it becomes $(4,-7)$.
For $(-4,-3)$: After reflection, it becomes $(4,-3)$.

Answer:

1. d. Reflection
2. c. $(4,-3),(4,-7),(2,-6)$