To determine the sequence of steps used to move the triangle \( ABC \) in Quadrant IV to the triangle \( EGH \) in Quadrant II, we analyze the positions of the triangles and how they can be transformed into each other.
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Finding the transformation direction:
- Triangle \( ABC \) has vertices at \( A(1, -1) \), \( B(1, -3) \), and \( C(4, -3) \).
- Triangle \( EGH \) has vertices at \( E(-2, 5) \), \( G(-2, 3) \), and \( H(-5, 3) \).
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Reflection to Quadrants:
- A reflection across the x-axis would take Triangle \( ABC \) from Quadrant IV to Quadrant III because it changes the sign of the y-coordinates.
- For Triangle \( ABC \) (which is originally in Quadrant IV), reflecting directly over the x-axis will first place it in Quadrant III, making the coordinates of the reflected points \( A'(1, 1) \), \( B'(1, 3) \), \( C'(4, 3) \).
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Mapping to Quadrant II:
- From Quadrant III (the reflected position) to Quadrant II involves a translation. The translation needed to move from \((1, 1)\) to \((-2, 5)\) can be calculated. This change can be represented as:
- \( x \) from \( 1 \) to \( -2 \): translates by \( -3 \)
- \( y \) from \( 1 \) to \( 5 \): translates by \( +4 \)
However, the simplest indication from the options given is that after reflecting it goes to Quadrant I, but that is not necessary based on our current findings.
- From Quadrant III (the reflected position) to Quadrant II involves a translation. The translation needed to move from \((1, 1)\) to \((-2, 5)\) can be calculated. This change can be represented as:
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Final adjustment:
- The transformation required based on perimeter data and a careful bitmap understanding leads to the confirmation that triangle rotation would allow moving the shape with less space consideration.
The correct answer to move triangle \( ABC \) into position of triangle \( EGH \) is:
reflection to Quadrant III, then a translation of \((-1, 6)\)