Use the image to answer the question.

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′(−1,3), and C′(−6,3)

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

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

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 the x-axis and y-axis, we need to apply the reflection transformations to each vertex of triangle ABC.

The original vertices of triangle ABC are:

• A(2, -1)
• B(6, -3)
• C(1, -3)

Reflecting across the x-axis:

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

Then reflecting these points across the y-axis:

• A(2, 1) becomes A′(-2, 1)
• B(6, 3) becomes B′(-6, 3)
• C(1, 3) becomes C′(-1, 3)

Thus, the coordinates of triangle A′B′C′ are:

• A′(-2, 1)
• B′(-6, 3)
• C′(-1, 3)

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