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′(−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) . 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′(−6,−3) , and C′(−1,−3)

Answer 1

To reflect a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃) first with respect to the x-axis, then with respect to the y-axis, we do the following:

1. **Reflecting across the x-axis**: This transforms the vertices as follows:
- A'(x₁, -y₁)
- B'(x₂, -y₂)
- C'(x₃, -y₃)

2. **Reflecting the resulting points across the y-axis**: This transforms the vertices as follows:
- A''(-x₁, -y₁)
- B''(-x₂, -y₂)
- C''(-x₃, -y₃)

Given that you provided the vertices of triangle ABC, which were not specified in the question, let's assume the original vertices are:
- A(x₁, y₁)
- B(x₂, y₂)
- C(x₃, y₃)

Now applying the reflections step-by-step:

After reflecting across the x-axis:
- A' = (x₁, -y₁)
- B' = (x₂, -y₂)
- C' = (x₃, -y₃)

After reflecting across the y-axis:
- A'' = (-x₁, -(-y₁)) = (-x₁, y₁)
- B'' = (-x₂, -(-y₂)) = (-x₂, y₂)
- C'' = (-x₃, -(-y₃)) = (-x₃, y₃)

From this transformation, you can see the final coordinates of the vertices of triangle A'B'C' are:
- A''(-x₁, y₁)
- B''(-x₂, y₂)
- C''(-x₃, y₃)

With the points you've provided:
- A'(-2, 1)
- B'(-6, 3)
- C'(-1, 3)

Reflecting these points would yield:
- A''(2, 1)
- B''(6, 3)
- C''(1, 3)

Making the final vertices of triangle A′B′C′:
- A′(2, 1)
- B′(6, 3)
- C′(1, 3)

So, the correct response is that the vertices of triangle A′B′C′ are A′(2, 1), B′(6, 3), and C′(1, 3).