Questions: Reflect triangle ABC over the line of reflection and label the image A'B'C'. Then translate A'B'C' 3 units to the right and 4 units down, Label the new image A"B"C".

Reflect triangle ABC over the line of reflection and label the image A'B'C'.

Then translate A'B'C' 3 units to the right and 4 units down, Label the new image A"B"C".
Transcript text: Reflect triangle $A B C$ over the line of reflection and label the image $A^{\prime} B^{\prime} C^{\prime}$. Then translate $A^{\prime} B^{\prime} C^{\prime} 3$ units to the right and 4 units down, Label the new image A"B"C"
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Solution

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Solution Steps

Step 1: Reflect Triangle ABC Over the Line of Reflection
  • Identify the coordinates of points A, B, and C.
    • A(-4, -3)
    • B(-2, 1)
    • C(1, -2)
  • Reflect these points over the line of reflection (y = x).
    • A'(-3, -4)
    • B'(1, -2)
    • C'(-2, 1)
Step 2: Translate A'B'C' 3 Units to the Right
  • Add 3 to the x-coordinates of A', B', and C'.
    • A''(-3 + 3, -4) = (0, -4)
    • B''(1 + 3, -2) = (4, -2)
    • C''(-2 + 3, 1) = (1, 1)
Step 3: Translate A'B'C' 4 Units Down
  • Subtract 4 from the y-coordinates of A'', B'', and C''.
    • A'''(0, -4 - 4) = (0, -8)
    • B'''(4, -2 - 4) = (4, -6)
    • C'''(1, 1 - 4) = (1, -3)

Final Answer

  • The coordinates of the final image A''B''C'' are:
    • A'''(0, -8)
    • B'''(4, -6)
    • C'''(1, -3)
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