Question

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 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′(−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′(−1,3)
, and C′(−6,3)
.

Answer 1

To reflect triangle ABC with respect to the x-axis and the y-axis, we need to follow these steps for each vertex:

1. Reflect across the x-axis:

   • For a point (x, y), the reflection across the x-axis is (x, -y).

2. Reflect across the y-axis:

   • For a point (x, y), the reflection across the y-axis is (-x, y).

Now, let's reflect each vertex 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)

Combining these results, the vertices of triangle A′B′C′ after reflecting first across the x-axis and then the y-axis will be:

• A'(-2, 1)
• B'(-6, 3)
• C'(-1, 3)

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

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