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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 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 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)
.

Answer 1

To reflect triangle ABC with vertices A(2, -1), B(6, -3), and C(1, -3) across the x-axis and then the y-axis, we follow these steps:

1. Reflect across the x-axis: To reflect a point (x, y) across the x-axis, the new coordinates become (x, -y).

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

2. Reflect across the y-axis: To reflect a point (x, y) across the y-axis, the new coordinates become (-x, y).

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

Thus, the final coordinates of the reflected vertices A'', B'', and C'' are:

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

Therefore, 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)."