Question

Identify the type of transformation that moves line FG to line F'G'.
An image displaying a line FG intersecting with line F'G'. The vertices of FG is F of -6 comma -3 and G of 3 comma 6. the vertice s of F'G' is F' of 6 comma -3 and G' of -3 comma 6. They intersect at 0 comma 3.
A.
Reflection over the x-axis
B.
Rotation
C.
Translation
D.
Reflection over the y-axis

Answer 1

To determine the type of transformation that moves line FG to line F'G', we need to analyze the coordinates provided.

The endpoints of line FG are:
- F(-6, -3)
- G(3, 6)

The endpoints of line F'G' are:
- F'(6, -3)
- G'(-3, 6)

Next, let's look at the transformation:

1. **F to F'**:
- The x-coordinate changes from -6 to 6 (a change of +12).
- The y-coordinate remains the same (-3).

2. **G to G'**:
- The x-coordinate changes from 3 to -3 (a change of -6).
- The y-coordinate remains the same (6).

From these observations, we can conclude the following about the transformation:
- The transformation involves a change in the x-coordinates but not in the y-coordinates for point F, and a reversal in the x-coordinates for point G.
- This suggests that there is reflection involved in relation to the y-axis, as the x-coordinates are being flipped.

Thus, the transformation that moves line FG to line F'G' is a **reflection over the y-axis**.

The correct answer is:
**D. Reflection over the y-axis**.