Question

select the correct sequences in the table.
figure 2 is the image of figure 1 after undergoing a sequence of transformations.
grid with two rectangles labeled 1 (orange) and 2 (pink), axes labeled x and y
which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent?
sequence 1:
figure 1 is first reflected over the line ( y = -x ) and then translated 8 units up and 2 units right to create figure 2.
sequence 2:
figure 1 is first translated down 10 units and then rotated ( 180^circ ) clockwise about the origin to create figure 2.
sequence 3:
figure 1 is first reflected across the x - axis and then rotated ( 180^circ ) clockwise about the origin? (text cut off)
sequence 4:
figure 1 is first rotated ( 90^circ ) counterclockwise about the origin and then translated 2 units text cut off

Explanation:

To determine the correct sequences, we analyze the transformations (reflection, translation, rotation) that map Figure 1 to Figure 2.

Analyzing Each Sequence:

• Sequence 1: Reflecting over \( y = -x \), then translating 8 units up and 2 units right.
• Sequence 2: Translating down 10 units, then rotating \( 180^\circ \) clockwise.
• Sequence 3: Reflecting over the \( x \)-axis, then rotating \( 180^\circ \) clockwise.
• Sequence 4: Rotating \( 90^\circ \) counterclockwise, then translating 2 units (incomplete, but likely a typo).

Key Observations:

Figure 1 (orange rectangle) and Figure 2 (pink rectangle) are congruent (same shape/size) and appear to be related by a reflection/rotation/translation.

Correct Sequences (Assuming Completion of Sequence 4):

• Sequence 1: Reflection over \( y = -x \) (swaps \( x \) and \( y \), flips signs) followed by translation aligns Figure 1 to Figure 2.
• Sequence 4: Rotating \( 90^\circ \) counterclockwise (changes coordinates \( (x,y) \to (-y,x) \)) and translating 2 units right/up (adjusting position) aligns Figure 1 to Figure 2.

Final Answer:

The two correct sequences are Sequence 1 and Sequence 4 (or other valid pairs based on complete analysis). If forced to choose from visible options (assuming Sequence 4 is complete), the most probable correct sequences are:

Answer:

Sequence 1 and Sequence 4 (or other valid pairs based on full transformation analysis).

(Note: The table appears partially cut off, but the core approach is analyzing congruence-preserving transformations: reflection, translation, rotation.)