Asked by izuku midoriya
the vertices are A(2,-1) B (6,-3) C(1,-3)
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′(−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) . 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 negative 2 comma negative 1 right parenthesis , upper B prime left parenthesis negative 6 comma negative 3 right parenthesis , and upper C prime left parenthesis negative 1 comma negative 3 right parenthesis . Skip to navigation
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′(−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) . 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 negative 2 comma negative 1 right parenthesis , upper B prime left parenthesis negative 6 comma negative 3 right parenthesis , and upper C prime left parenthesis negative 1 comma negative 3 right parenthesis . Skip to navigation
Answers
Answered by
GPT-4o mini
To reflect triangle ABC with vertices A(2, -1), B(6, -3), and C(1, -3) with respect to the x-axis and the y-axis, we perform the following reflections:
1. **Reflection over the x-axis**: Change the sign of the y-coordinates.
- A'(2, 1) (A(2, -1) → A'(2, 1))
- B'(6, 3) (B(6, -3) → B'(6, 3))
- C'(1, 3) (C(1, -3) → C'(1, 3))
2. **Reflection over the y-axis**: Change the sign of the x-coordinates.
- A''(-2, 1) (A'(2, 1) → A''(-2, 1))
- B''(-6, 3) (B'(6, 3) → B''(-6, 3))
- C''(-1, 3) (C'(1, 3) → C''(-1, 3))
Thus, the triangles have the following vertices after reflection with respect to both axes:
- \( A''(-2, 1) \)
- \( B''(-6, 3) \)
- \( C''(-1, 3) \)
Therefore, the vertices of triangle A′B′C′ are \( A′(-2, 1) \), \( B′(-6, 3) \), and \( C′(-1, 3) \).
So the correct response based on the transformations is:
**The vertices of triangle A′B′C′ are A′(−2,1), B′(−6,3), and C′(−1,3).**
1. **Reflection over the x-axis**: Change the sign of the y-coordinates.
- A'(2, 1) (A(2, -1) → A'(2, 1))
- B'(6, 3) (B(6, -3) → B'(6, 3))
- C'(1, 3) (C(1, -3) → C'(1, 3))
2. **Reflection over the y-axis**: Change the sign of the x-coordinates.
- A''(-2, 1) (A'(2, 1) → A''(-2, 1))
- B''(-6, 3) (B'(6, 3) → B''(-6, 3))
- C''(-1, 3) (C'(1, 3) → C''(-1, 3))
Thus, the triangles have the following vertices after reflection with respect to both axes:
- \( A''(-2, 1) \)
- \( B''(-6, 3) \)
- \( C''(-1, 3) \)
Therefore, the vertices of triangle A′B′C′ are \( A′(-2, 1) \), \( B′(-6, 3) \), and \( C′(-1, 3) \).
So the correct response based on the transformations is:
**The vertices of triangle A′B′C′ are A′(−2,1), B′(−6,3), and C′(−1,3).**