Question

Use the image to answer the 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 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)
.
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 .

Answer 1

To reflect triangle ABC over the x-axis and then the y-axis, we can follow these steps for each vertex of the triangle.

The coordinates of the vertices of triangle ABC are:
- A(2, -1)
- B(6, -3)
- C(1, -3)

1. **Reflect over the x-axis**: To reflect a point (x, y) over the x-axis, we change the sign of the y-coordinate.
- A'(2, 1) (from A(2, -1))
- B'(6, 3) (from B(6, -3))
- C'(1, 3) (from C(1, -3))

2. **Reflect over the y-axis**: To reflect a point (x, y) over the y-axis, we change the sign of the x-coordinate.
- A''(-2, 1) (from A'(2, 1))
- B''(-6, 3) (from B'(6, 3))
- C''(-1, 3) (from C'(1, 3))

Thus, the vertices of triangle A''B''C'' (or triangle A'B'C') after both reflections are:
- A''(-2, 1)
- B''(-6, 3)
- C''(-1, 3)

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