Given the following points determine whether the transformation was a Rotation(specify direction and size), a reflection(over what point/line) or trasnlation(specify the rule).

1.
C(0,4). C'(2,6) N(-2,3) N'(0,5)

2.
G(0,0) G'(4,0) R(-1,4) R'(5,4)

3.
K(-4,-2) K'(4,-2) V(1,1) V'(9,1)

To determine whether the given transformations are rotations, reflections, or translations, you need to look at how the points have moved and analyze the patterns.

1. C(0,4), C'(2,6), N(-2,3), N'(0,5):

You can observe that the x and y coordinates of both pairs of points have changed by the same amount. Specifically, (x, y) → (x + 2, y + 2) for each point. This indicates a translation. In this case, the transformation is a translation of vector (2, 2) because each point has moved 2 units to the right and 2 units up.

Therefore, the transformation is a translation with the rule T(x, y) → (x + 2, y + 2).

2. G(0,0), G'(4,0), R(-1,4), R'(5,4):

For this set of points, you can notice that the y coordinates of both pairs of points remain the same, but the x coordinates change. Additionally, the y coordinate is constant throughout. This pattern suggests a reflection over the y-axis because the x-axis flips.

Hence, the transformation is a reflection over the y-axis.

3. K(-4,-2), K'(4,-2), V(1,1), V'(9,1):

In this scenario, the y coordinates of the points remain constant, but the x coordinates change. Also, the x coordinate of each point has changed by the same amount. This pattern indicates a translation since the points are shifted horizontally.

Consequently, the transformation is a translation with the rule T(x, y) → (x + 8, y).

To summarize:
1. Translation with rule T(x, y) → (x + 2, y + 2).
2. Reflection over the y-axis.
3. Translation with rule T(x, y) → (x + 8, y).