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.

Question

Reflect triangle ABC with respect to the x-axis and the y-axis. What are the vertices of triangle A'B'C'?

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′(−1,3)
, and C′(−6,3)
.

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 over the x-axis and then the y-axis, we follow these steps:

1. Reflect over the x-axis:

   • The reflection of a point \((x, y)\) over the x-axis is \((x, -y)\).
   • For the vertices of triangle ABC:
     • A(2, -1) becomes A'(2, 1)
     • B(6, -3) becomes B'(6, 3)
     • C(1, -3) becomes C'(1, 3)

2. Reflect over the y-axis:

   • The reflection of a point \((x, y)\) over the y-axis is \((-x, y)\).
   • Applying this to the reflected points A', B', and C':
     • A'(2, 1) becomes A''(-2, 1)
     • B'(6, 3) becomes B''(-6, 3)
     • C'(1, 3) becomes C''(-1, 3)

Thus, the vertices of triangle A'B'C' after reflecting triangle ABC first over the x-axis and then the y-axis are:

• A'(-2, 1)
• B'(-6, 3)
• C'(-1, 3)

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