Triangle ABC is shown. A is at negative 2, 1. B is at negative 1, 4. C is at negative 4, 5. If triangle ABC is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees, where will point A' lie? (−1, 2) (−2, 1) (1, −2) (2, −1)

Answer:

B (-2,1)

Step-by-step explanation:

When you reflect over x axis the coordinates go from -2,1 to 2,1. When we rotate it 180, they go from 2,1 to -2,1. Point A will be at the same spot

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Point A' will lie at (b) (-2,1) after the transformation.

The coordinates of the triangle are given as:

[tex]A = (-2,1)[/tex]

[tex]B = (-1,4)[/tex]

[tex]C = (-4,5)[/tex]

The rule of reflection over the y-axis is:

[tex](x,y) \to (-x,y)[/tex]

So, the new coordinate of A is:

[tex]A =(2,1)[/tex]

The rule of reflection over the x-axis is:

[tex](x,y) \to (x,-y)[/tex]

So, the new coordinate of A is:

[tex]A =(2,-1)[/tex]

The rule of 180 degrees rotation is:

[tex](x,y) \to (-x,-y)[/tex]

So, the new coordinate of A is:

[tex]A = (-2,1)[/tex]

Hence, point A' will lie at (b) (-2,1)

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