Question

U4 L9 Question 3
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Question
Using triangle ABC with coordinates A(5,3) B(-2,7) C(-3,-8). Translate the triangle 3 units left and 6 units up and then reflect across the line x=-3. What are the coordinates of A''?(1 point)
Responses

(-2,7)
(-2,7)

(-10,-11)
(-10,-11)

(0,3)
(0,3)

(-8,9)

Answer 1

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:

1. **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).

2. **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)**