Question

triangle def has vertices at d(-1, 2), e(1, 4), and f(-1, 6). match the correct final coordinates to each transformation sequence.
answer choices:
(5, -1),(3, -3),(5, -5) (-4, 0),(-2, -2),(-4, -4) (1, -3),(3, -5),(1, -7) (-2, 1),(-4, -1),(-6, 1)
drag the answer choices to the correct category over here!
reflect across y-axis → rotate 90° counterclockwise
translate 3 left, 2 down → reflect across x-axis
rotate 180° around origin → translate 4 right, 1 up
reflect across x-axis → translate 2 right, 1 down

Explanation:

Reflect across \( y \)-axis \( \to \) Rotate \( 90^{\circ} \) counterclockwise

• For point \( D(-1,2) \):
• Reflect across \( y \)-axis: \( (1,2) \)
• Rotate \( 90^{\circ} \) counterclockwise: \( (-2,1) \)
• For point \( E(1,4) \):
• Reflect across \( y \)-axis: \( (-1,4) \)
• Rotate \( 90^{\circ} \) counterclockwise: \( (-4,-1) \)
• For point \( F(-1,6) \):
• Reflect across \( y \)-axis: \( (1,6) \)
• Rotate \( 90^{\circ} \) counterclockwise: \( (-6,1) \)
• Final coordinates: \( [(-2,1),(-4,-1),(-6,1)] \)

Translate 3 left, 2 down \( \to \) Reflect across \( x \)-axis

• For point \( D(-1,2) \):
• Translate 3 left, 2 down: \( (-4,0) \)
• Reflect across \( x \)-axis: \( (-4,0) \)
• For point \( E(1,4) \):
• Translate 3 left, 2 down: \( (-2,2) \)
• Reflect across \( x \)-axis: \( (-2,-2) \)
• For point \( F(-1,6) \):
• Translate 3 left, 2 down: \( (-4,4) \)
• Reflect across \( x \)-axis: \( (-4,-4) \)
• Final coordinates: \( [(-4,0),(-2,-2),(-4,-4)] \)

Rotate \( 180^{\circ} \) around origin \( \to \) Translate 4 right, 1 up

• For point \( D(-1,2) \):
• Rotate \( 180^{\circ} \): \( (1,-2) \)
• Translate 4 right, 1 up: \( (5,-1) \)
• For point \( E(1,4) \):
• Rotate \( 180^{\circ} \): \( (-1,-4) \)
• Translate 4 right, 1 up: \( (3,-3) \)
• For point \( F(-1,6) \):
• Rotate \( 180^{\circ} \): \( (1,-6) \)
• Translate 4 right, 1 up: \( (5,-5) \)
• Final coordinates: \( [(5,-1),(3,-3),(5,-5)] \)

Reflect across \( x \)-axis \( \to \) Translate 2 right, 1 down

• For point \( D(-1,2) \):
• Reflect across \( x \)-axis: \( (-1,-2) \)
• Translate 2 right, 1 down: \( (1,-3) \)
• For point \( E(1,4) \):
• Reflect across \( x \)-axis: \( (1,-4) \)
• Translate 2 right, 1 down: \( (3,-5) \)
• For point \( F(-1,6) \):
• Reflect across \( x \)-axis: \( (-1,-6) \)
• Translate 2 right, 1 down: \( (1,-7) \)
• Final coordinates: \( [(1,-3),(3,-5),(1,-7)] \)

Answer:

• Reflect across \( y \)-axis \( \to \) Rotate \( 90^{\circ} \) counterclockwise: \( [(-2,1),(-4,-1),(-6,1)] \)
• Translate 3 left, 2 down \( \to \) Reflect across \( x \)-axis: \( [(-4,0),(-2,-2),(-4,-4)] \)
• Rotate \( 180^{\circ} \) around origin \( \to \) Translate 4 right, 1 up: \( [(5,-1),(3,-3),(5,-5)] \)
• Reflect across \( x \)-axis \( \to \) Translate 2 right, 1 down: \( [(1,-3),(3,-5),(1,-7)] \)