Question

A= 2,-1
B= 6,-3
C=1,-3
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 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 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)
.

Answer 1

To reflect the triangle ABC across the x-axis and the y-axis, we can follow these steps:

1. **Reflect across the x-axis**: This changes the y-coordinates of each vertex to their negatives.
2. **Reflect across the y-axis**: This changes the x-coordinates of each vertex to their negatives.

Let's apply these transformations to each vertex of triangle ABC:

**Original Vertices:**
- A = (2, -1)
- B = (6, -3)
- C = (1, -3)

**Step 1: Reflect across the x-axis:**
- A: (2, -(-1)) = (2, 1)
- B: (6, -(-3)) = (6, 3)
- C: (1, -(-3)) = (1, 3)

**Step 2: Reflect across the y-axis:**
- A': (-2, 1)
- B': (-6, 3)
- C': (-1, 3)

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