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Use the image to answer the question. Reflect triangle ABC with respect to the x -axis and the y -axis. What are the vertices of triangle A′B′C′ ? (1 point)

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) .

1 answer

To reflect a triangle across the x-axis and the y-axis, we need to modify the coordinates of each vertex.

  1. Reflect across the x-axis: Change the sign of the y-coordinate.
  2. Reflect across the y-axis: Change the sign of the x-coordinate.

Given the original vertices of triangle ABC:

  • A(2, 1)
  • B(1, 3)
  • C(6, 3)

Step 1: Reflect across the x-axis:

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

Step 2: Reflect across the y-axis:

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

Therefore, the vertices of triangle A′B′C′ are:

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

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