Identify the type of transformation that moves line FG to line F'G'.

Question

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.