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

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′(−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 . The vertices of triangle A′B′C′ are A′(−2,1) , B′(−1,3) , and C′(−6,3) .

Answer 1

To find the vertices of triangle ABC after reflecting it with respect to the x-axis and then the y-axis, we can follow these steps for each vertex:

1. Reflecting across the x-axis: The reflection of a point \((x, y)\) across the x-axis is \((x, -y)\).
2. Reflecting across the y-axis: The reflection of a point \((x, y)\) across the y-axis is \((-x, y)\).

Now, let's apply these transformations to the points A(2, -1), B(6, -3), and C(1, -3):

1. Point A (2, -1):

   • Reflect across the x-axis: \(A(2, -1) \rightarrow A'(2, 1)\)
   • Reflect across the y-axis: \(A'(2, 1) \rightarrow A''(-2, 1)\)

2. Point B (6, -3):

   • Reflect across the x-axis: \(B(6, -3) \rightarrow B'(6, 3)\)
   • Reflect across the y-axis: \(B'(6, 3) \rightarrow B''(-6, 3)\)

3. Point C (1, -3):

   • Reflect across the x-axis: \(C(1, -3) \rightarrow C'(1, 3)\)
   • Reflect across the y-axis: \(C'(1, 3) \rightarrow C''(-1, 3)\)

Thus, the final vertices of triangle A'B'C' after reflecting triangle ABC first across the x-axis and then the y-axis are:

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

Therefore, the correct response is: The vertices of triangle \(A'B'C'\) are \(A'(-2, 1)\), \(B'(-6, 3)\), and \(C'(-1, 3)\).