Option D: [tex]B(2,-2) \rightarrow B^{\prime}(2,2)[/tex] is the pair of points which does not have y - axis as the line of reflection.
Explanation:
The translation rule to reflect the pair of points across the y - axis is given by
[tex](x,y)\implies (-x,y)[/tex]
Option A: [tex]B(3,-8) \rightarrow B^{\prime}(-3,-8)[/tex]:
Let us translate the coordinate B(3,-8) across y - axis using the translation rule [tex](x,y)\implies (-x,y)[/tex], we get,
[tex](3,-8)\implies (-3,-8)[/tex]
Thus, we get, [tex]B(3,-8) \rightarrow B^{\prime}(-3,-8)[/tex]
Hence, the pair of points [tex]B(3,-8) \rightarrow B^{\prime}(-3,-8)[/tex] has the line of reflection across y - axis.
Therefore, Option A is not the correct answer.
Option B: [tex]B(-6,2) \rightarrow B^{\prime}(6,2)[/tex]:
Let us translate the coordinate B(-6,2) across y - axis using the translation rule [tex](x,y)\implies (-x,y)[/tex], we get,
[tex](-6,2)\implies (6,2)[/tex]
Thus, we get, [tex]B(-6,2) \rightarrow B^{\prime}(6,2)[/tex]
Hence, the pair of points [tex]B(-6,2) \rightarrow B^{\prime}(6,2)[/tex] has the line of reflection across y - axis.
Therefore, Option B is not the correct answer.
Option C: [tex]B(5,-7) \rightarrow B^{\prime}(-5,-7)[/tex]:
Let us translate the coordinate B(5,-7) across y - axis using the translation rule [tex](x,y)\implies (-x,y)[/tex], we get,
[tex](5,-7)\implies (-5,-7)[/tex]
Thus, we get, [tex]B(5,-7) \rightarrow B^{\prime}(-5,-7)[/tex]
Hence, the pair of points [tex]B(5,-7) \rightarrow B^{\prime}(-5,-7)[/tex] has the line of reflection across y - axis.
Therefore, Option C is not the correct answer.
Option D: [tex]B(2,-2) \rightarrow B^{\prime}(2,2)[/tex]:
Let us translate the coordinate B(2,-2) across y - axis using the translation rule [tex](x,y)\implies (-x,y)[/tex], we get,
[tex](2,-2)\implies (-2,-2)[/tex]
Thus, we get, [tex]B(2,-2) \rightarrow B^{\prime}(-2,-2)[/tex]
Hence, the pair of points [tex]B(2,-2) \rightarrow B^{\prime}(2,2)[/tex] does not has the line of reflection across y - axis.
Therefore, Option D is the correct answer.
