the vertices are A(2,-1) B (6,-3) C(1,-3)

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) 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 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) . 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) . 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 . Skip to navigation

Answer 1

To reflect triangle ABC with vertices A(2, -1), B(6, -3), and C(1, -3) with respect to the x-axis and the y-axis, we perform the following reflections:

1. Reflection over the x-axis: Change the sign of the y-coordinates.

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

2. Reflection over the y-axis: Change the sign of the x-coordinates.

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

Thus, the triangles have the following vertices after reflection with respect to both axes:

• $A^{″}(-2,1)$
• $B^{″}(-6,3)$
• $C^{″}(-1,3)$

Therefore, the vertices of triangle A′B′C′ are $A\prime (-2,1)$, $B\prime (-6,3)$, and $C\prime (-1,3)$.

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