Question

If triangle ABC is reflected over the y‐axis, reflected over the x‐axis, and rotated 180 degrees, where will point A' lie?

Answer 1

Given that ABC is a triangle and is reflected over the y - axis, reflected over the x - axis and rotated 180°

We need to determine the coordinates of the point A'

Reflection over the y - axis:

The coordinates of the point A is (-2,1)

The transformation rule to reflect across the y - axis is $(x,y)\rightarrow (-x,y)$

Substituting the point (-2,1) in the rule, we get;

$(-2,1)\rightarrow (2,1)$

Thus, the coordinates of the point A after reflection over the y - axis is (2,1)

Reflection over the x - axis:

The transformation rule to reflect across the x - axis is $(x,y)\rightarrow (x,-y)$

Substituting the point (2,1) in the rule, we get;

$(2,1)\rightarrow (2,-1)$

Thus, the coordinates of the point A after reflection over the x - axis is (2,-1)

Rotation about 180°:

The transformation rule to rotate about 180° is $(x,y)\rightarrow (-x,-y)$

Substituting the point (2,-1) in the rule, we get;

$(2,-1)\rightarrow (-2,1)$

Thus, the coordinates of the point A after the rotation about 180° is (-2,1)

Therefore, the coordinates of the point A' is (-2,1)

Hence, Option B is the correct answer.