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Question

An illustration of a coordinate plane with four quadrants shows the x-axis extending from negative 9 to 9 in increments of 1 and the y-axis extending from negative 11 to 11 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma negative 1 right parenthesis, B left parenthesis 6 comma negative 3 right parenthesis, and C left parenthesis 1 comma negative 3 right parenthesis.

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 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)
.
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 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 .
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Answer 1

To reflect triangle \( ABC \) over the \( x \)-axis and the \( y \)-axis, we will perform the following transformations on each vertex of the triangle:

1. Reflection across the \( x \)-axis: For a point \( (x, y) \), the reflection across the \( x \)-axis is \( (x, -y) \).

2. Reflection across the \( y \)-axis: For a point \( (x, y) \), the reflection across the \( y \)-axis is \( (-x, y) \).

We can reflect the vertices of triangle \( ABC \):

• Vertex \( A(2, -1) \):

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

• Vertex \( B(6, -3) \):

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

• Vertex \( C(1, -3) \):

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

Thus, the vertices of triangle \( A'B'C' \) after reflecting across both axes are:

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

Hence, the correct response is:

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