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 the type of transformation for each set of points, we need to analyze the changes in their coordinates. Here's how you can approach each problem:

1. For the first set of points (C, C', N, N'), we can calculate the differences in the x and y coordinates for each pair.

- Δx = C'x - Cx = 2 - 0 = 2
- Δy = C'y - Cy = 6 - 4 = 2

Since both Δx and Δy have the same value, 2, it indicates a translation. To specify the rule of this translation, we can simply state that all points have been shifted 2 units to the right and 2 units up.

2. For the second set of points (G, G', R, R'), let's do the same calculations:

- Δx = G'x - Gx = 4 - 0 = 4
- Δy = G'y - Gy = 0 - 0 = 0

Here, we notice that Δx has a value of 4, while Δy is 0. This indicates a translation as well. The rule for this translation is that all points have been shifted 4 units to the right.

3. Lastly, for the third set of points (K, K', V, V'):

- Δx = K'x - Kx = 4 - (-4) = 8
- Δy = K'y - Ky = -2 - (-2) = 0

Similar to the second case, Δx has a value of 8, while Δy is 0. Therefore, this is also a translation, but in this case, the points have been shifted 8 units to the right.

So, to summarize the types and rules of transformation for each set of points:

1. Translation: All points shifted 2 units to the right and 2 units up.
2. Translation: All points shifted 4 units to the right.
3. Translation: All points shifted 8 units to the right.