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 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′(−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 both the x-axis and the y-axis, we need to apply the reflection rules:

1. Reflection across the x-axis: The point \( (x, y) \) becomes \( (x, -y) \).
2. Reflection across the y-axis: The point \( (x, y) \) becomes \( (-x, y) \).

When reflecting a point across both axes, we can combine the transformations as follows:

For a point \( (x, y) \):

• Reflecting across the x-axis gives us \( (x, -y) \).
• Reflecting that result across the y-axis gives us \( (-x, -y) \).

Thus, to find the coordinates of \( A', B', \) and \( C' \), we can reflect \( A, B, \) and \( C \) using this combined transformation.

However, we need the original coordinates of \( A, B, \) and \( C \) to perform this. Since they are not provided in your question, I can't compute the result directly.

If you could provide the original coordinates of points \( A, B, \) and \( C \), I would be able to reflect them and determine the vertices of triangle \( A'B'C' \).