Question

Use the image to answer the question.
A Cartesian coordinate plane shows an original triangle and two transformed versions across all four quadrants.

How would you describe this series of transformations?

(1 point)
Responses

Reflection across the y
-axis and then a translation of (−3,−5)
shows that triangle ABC
is congruent to triangle A′′B"C"
.
Reflection across the y -axis and then a translation of left parenthesis negative 3 comma negative 5 right parenthesis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .

Since triangles ABC
and A′′B"C"
do not have the same orientation, they are not congruent.
Since triangles upper A upper B upper C and upper A double prime upper B double prime upper C double prime do not have the same orientation, they are not congruent.

Translation of (2,0)
and then reflection across the x
-axis shows that triangle ABC
is congruent to triangle A′′B"C"
.
Translation of left parenthesis 2 comma 0 right parenthesis and then reflection across the x -axis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .

Rotation of 90 degrees clockwise and then reflection across the x
-axis shows that triangle ABC
is congruent to triangle A′′B"C"
.
Rotation of 90 degrees clockwise and then reflection across the x -axis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .
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Answer 1

I can’t see the diagram you’re referring to. Could you either upload the image or give the coordinates of triangle ABC and A″B″C″ (or of any one pair of corresponding vertices)?

If you want to check it yourself, here are quick tests for each proposed sequence:

- Reflection across the y-axis then translation by (−3, −5):
1. Reflect a vertex (x,y) across the y-axis → (−x,y).
2. Translate by (−3,−5) → (−x−3, y−5).
3. If each vertex of A″B″C″ equals (−x−3, y−5) for the corresponding vertex (x,y) of ABC, the sequence is correct.

- Translation by (2,0) then reflection across the x-axis:
1. Translate (x,y) by (2,0) → (x+2,y).
2. Reflect across the x-axis → (x+2, −y).
3. If A″B″C″ matches those coordinates, this sequence is correct.

- Rotation 90° clockwise then reflection across the x-axis:
1. Rotate (x,y) 90° clockwise → (y, −x).
2. Reflect across the x-axis → (y, x).
3. If each vertex of A″B″C″ equals (y,x) for the corresponding (x,y), that sequence is correct.

Also: note that reflections and rotations preserve congruence; orientation (clockwise vs counterclockwise listing) may change under a reflection but triangles are still congruent.

Send the image or coordinates and I’ll identify the correct option.