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Given the following points:
[tex]\[
\begin{array}{l}
A(2,1) \\
B(-3,4) \\
C(0,0)
\end{array}
\][/tex]

Perform a translation using the rule [tex]\((x+2, y-1)\)[/tex] and give the location of the new points.



Answer :

GinnyAnswer
Sure! To perform a translation on the given points using the rule \((x+2, y-1)\), we will apply the translation rule to the coordinates of each point step by step.

### Point A (2,1):

1. Original coordinates of A: \((2, 1)\)
2. Translation rule: \((x + 2, y - 1)\)
3. New x-coordinate: \(2 + 2 = 4\)
4. New y-coordinate: \(1 - 1 = 0\)
5. New coordinates of A: \((4, 0)\)

### Point B (-3,4):

1. Original coordinates of B: \((-3, 4)\)
2. Translation rule: \((x + 2, y - 1)\)
3. New x-coordinate: \(-3 + 2 = -1\)
4. New y-coordinate: \(4 - 1 = 3\)
5. New coordinates of B: \((-1, 3)\)

### Point C (0,0):

1. Original coordinates of C: \((0, 0)\)
2. Translation rule: \((x + 2, y - 1)\)
3. New x-coordinate: \(0 + 2 = 2\)
4. New y-coordinate: \(0 - 1 = -1\)
5. New coordinates of C: \((2, -1)\)

### Summary

The new coordinates after performing the translation are:

- \( A' = (4, 0) \)
- \( B' = (-1, 3) \)
- \( C' = (2, -1) \)

Thus, the translated points are:
[tex]\[ \begin{array}{l} A'(4, 0) \\ B'(-1, 3) \\ C'(2, -1) \end{array} \][/tex]

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