To find the coordinates of A'' after performing the specified transformations on triangle ABC with coordinates A(5, 3), B(-2, 7), and C(-3, -8), we will follow these steps:
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Translate the triangle 3 units left and 6 units up.
- Translation: To translate a point (x, y) left by 3 units, we subtract 3 from the x-coordinate, and to move it up by 6 units, we add 6 to the y-coordinate.
- For point A(5, 3):
- New x-coordinate: \( 5 - 3 = 2 \)
- New y-coordinate: \( 3 + 6 = 9 \)
- So after the translation, A' is at (2, 9).
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Reflect across the line x = -3.
- Reflection: When a point (x, y) is reflected across the vertical line x = -3, we can find the new x-coordinate by calculating the distance from the point to the line and adjusting accordingly.
- Distance from A'(2, 9) to the line x = -3: \( 2 - (-3) = 5 \) (the distance is positive as A' is to the right of the line).
- To reflect, we subtract this distance from -3:
- New x-coordinate: \( -3 - 5 = -8 \)
- The y-coordinate remains the same.
- Therefore, A'' is at (-8, 9).
The final coordinates of A'' are:
(-8, 9)
Among the given responses, the correct answer is:
(-8, 9)