use a arrow notation to write a rule for this translation

(2,1) (5,3) (-1,4) ?

can someone answer pls?

To use arrow notation to write a rule for this translation, we need to determine the pattern of the translation between the given points.

Let's compare the x-coordinates and y-coordinates individually:

For the x-coordinate, the translation appears to be adding 3 to each value:
2 → 2 + 3 = 5
5 → 5 + 3 = 8
-1 → -1 + 3 = 2

For the y-coordinate, the translation seems to be adding 2 to each value:
1 → 1 + 2 = 3
3 → 3 + 2 = 5
4 → 4 + 2 = 6

Based on this pattern, we can write the rule for the translation using arrow notation as follows:

(2,1) → (5,3) → (8,5) → ...

Therefore, the next point after (-1,4) would be (-1 + 3, 4 + 2) = (2, 6).

To write a rule for a translation using arrow notation, we need to determine the horizontal and vertical shifts.

Given the original points (2,1), (5,3), and (-1,4), we can determine the horizontal and vertical shifts by comparing corresponding coordinates.

Horizontal Shift:
- We can see that the x-coordinate of the first point changed from 2 to 5, which indicates a rightward shift of 3 units.
- The x-coordinate of the second point changed from 5 to -1, indicating a leftward shift of 6 units.

Vertical Shift:
- The y-coordinate of the first point changed from 1 to 3, indicating an upward shift of 2 units.
- The y-coordinate of the second point changed from 3 to 4, indicating an upward shift of 1 unit.

Therefore, the rule for this translation can be written using arrow notation as follows:

(x, y) → (x + 6, y + 2)

Thus, applying this rule to the original points, we can find the translated point by adding 6 to the x-coordinate and 2 to the y-coordinate.

is (2,1) supposed to end up at (-1,4)?

If so, why the intermediate point? The final translation is just

(x,y) -> (x-3,y+3)