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'
<u>Reflection over the y - axis:</u>
The coordinates of the point A is (-2,1)
The transformation rule to reflect across the y - axis is ![(x,y)\rightarrow (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-x%2Cy%29)
Substituting the point (-2,1) in the rule, we get;
![(-2,1)\rightarrow (2,1)](https://tex.z-dn.net/?f=%28-2%2C1%29%5Crightarrow%20%282%2C1%29)
Thus, the coordinates of the point A after reflection over the y - axis is (2,1)
<u>Reflection over the x - axis:</u>
The transformation rule to reflect across the x - axis is ![(x,y)\rightarrow (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28x%2C-y%29)
Substituting the point (2,1) in the rule, we get;
![(2,1)\rightarrow (2,-1)](https://tex.z-dn.net/?f=%282%2C1%29%5Crightarrow%20%282%2C-1%29)
Thus, the coordinates of the point A after reflection over the x - axis is (2,-1)
<u>Rotation about 180°:</u>
The transformation rule to rotate about 180° is ![(x,y)\rightarrow (-x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-x%2C-y%29)
Substituting the point (2,-1) in the rule, we get;
![(2,-1)\rightarrow (-2,1)](https://tex.z-dn.net/?f=%282%2C-1%29%5Crightarrow%20%28-2%2C1%29)
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.