Use the image to answer the question. Reflect triangle ABC with respect to the x -axis and the y -axis. What are the vertices of triangle A′B′C′ ? (1 point) Responses The vertices of triangle A′B′C′ are A′(−2,1) , B′(−6,3) , and C′(−1,3) . The vertices of triangle upper A prime upper B prime upper C prime are upper A prime left parenthesis negative 2 comma 1 right parenthesis , upper B prime left parenthesis negative 6 comma 3 right parenthesis , and upper C prime left parenthesis negative 1 comma 3 right parenthesis . The vertices of triangle A′B′C′ are A′(2,1) , B′(6,3) , and C′(1,3) . The vertices of triangle upper A prime upper B prime upper C prime are upper A prime left parenthesis 2 comma 1 right parenthesis , upper B prime left parenthesis 6 comma 3 right parenthesis , and upper C prime left parenthesis 1 comma 3 right parenthesis . The vertices of triangle A′B′C′ are A′(−2,1) , B′(−1,3) , and C′(−6,3) . The vertices of triangle upper A prime upper B prime upper C prime are upper A prime left parenthesis negative 2 comma 1 right parenthesis , upper B prime left parenthesis negative 1 comma 3 right parenthesis , and upper C prime left parenthesis negative 6 comma 3 right parenthesis . The vertices of triangle A′B′C′ are A′(−2,−1) , B′(−6,−3) , and C′(−1,−3) .

Answer 1

To find the vertices of triangle \( A'B'C' \) after reflecting triangle \( ABC \) across the x-axis and the y-axis, we follow these steps:

1. Reflect across the x-axis: This changes the sign of the y-coordinate of each vertex.
2. Reflect across the y-axis: This changes the sign of the x-coordinate of each vertex.

Assuming the original coordinates of the triangle vertices are:

• \( A(x_A, y_A) \)
• \( B(x_B, y_B) \)
• \( C(x_C, y_C) \)

Reflecting each point:

• \( A' = (-x_A, -y_A) \)
• \( B' = (-x_B, -y_B) \)
• \( C' = (-x_C, -y_C) \)

Now, we need to analyze the given options for triangle \( A'B'C' \):

1. Reflecting the points (outcomes):
   • If \( A(-2,1) \), then reflecting gives \( A' = (2,-1) \).
   • If \( B(-6,3) \), then reflecting gives \( B' = (6,-3) \).
   • If \( C(-1,3) \), then reflecting gives \( C' = (1,-3) \).

Now let's analyze the responses:

1. \( A'(-2, 1), B'(-6, 3), C'(-1, 3) \)
2. \( A'(2, 1), B'(6, 3), C'(1, 3) \)
3. \( A'(-2, 1), B'(-1, 3), C'(-6, 3) \)
4. \( A'(-2, -1), B'(-6, -3), C'(-1, -3) \)

The correct reflection results are not given on the list provided. The correct transformation steps lead to:

• If the original coordinates are not listed, we specifically cannot choose. However, double-checking the transformations can lead to misreporting.

Please confirm your initial triangle coordinates for a clear choice or clarification on which transformation approach/articulation was noted for the original triangle vertices.

Answer 2

A is (2, -1) B is (6, -3), and C is (1, -3)

Answer 3

Thank you for providing the coordinates of the vertices of triangle \( ABC \):

• \( A(2, -1) \)
• \( B(6, -3) \)
• \( C(1, -3) \)

Now, let's reflect triangle \( ABC \) across the x-axis and the y-axis:

1. Reflect across the x-axis:

   • \( A(2, -1) \) becomes \( A'(2, 1) \)
   • \( B(6, -3) \) becomes \( B'(6, 3) \)
   • \( C(1, -3) \) becomes \( C'(1, 3) \)

2. Now, reflect across the y-axis:

   • \( A'(2, 1) \) becomes \( A''(-2, 1) \)
   • \( B'(6, 3) \) becomes \( B''(-6, 3) \)
   • \( C'(1, 3) \) becomes \( C''(-1, 3) \)

The final vertices of triangle \( A'B'C' \) after reflecting across both axes are:

• \( A''(-2, 1) \)
• \( B''(-6, 3) \)
• \( C''(-1, 3) \)

Thus, the answer is:

The vertices of triangle \( A'B'C' \) are \( A'(-2, 1), B'(-6, 3), C'(-1, 3) \).

This matches the response:

• The vertices of triangle \( A'B'C' \) are \( A'(-2, 1) \), \( B'(-6, 3) \), \( C'(-1, 3) \).