Question

12. The y-axis is NOT the line of reflection for which pair of points?

Answer 1

Option D: $B(2,-2) \rightarrow B^{\prime}(2,2)$ 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

$(x,y)\implies (-x,y)$

Option A: $B(3,-8) \rightarrow B^{\prime}(-3,-8)$:

Let us translate the coordinate B(3,-8) across y - axis using the translation rule $(x,y)\implies (-x,y)$, we get,

$(3,-8)\implies (-3,-8)$

Thus, we get, $B(3,-8) \rightarrow B^{\prime}(-3,-8)$

Hence, the pair of points $B(3,-8) \rightarrow B^{\prime}(-3,-8)$ has the line of reflection across y - axis.

Therefore, Option A is not the correct answer.

Option B: $B(-6,2) \rightarrow B^{\prime}(6,2)$:

Let us translate the coordinate B(-6,2) across y - axis using the translation rule $(x,y)\implies (-x,y)$, we get,

$(-6,2)\implies (6,2)$

Thus, we get, $B(-6,2) \rightarrow B^{\prime}(6,2)$

Hence, the pair of points $B(-6,2) \rightarrow B^{\prime}(6,2)$ has the line of reflection across y - axis.

Therefore, Option B is not the correct answer.

Option C: $B(5,-7) \rightarrow B^{\prime}(-5,-7)$:

Let us translate the coordinate B(5,-7) across y - axis using the translation rule $(x,y)\implies (-x,y)$, we get,

$(5,-7)\implies (-5,-7)$

Thus, we get, $B(5,-7) \rightarrow B^{\prime}(-5,-7)$

Hence, the pair of points $B(5,-7) \rightarrow B^{\prime}(-5,-7)$ has the line of reflection across y - axis.

Therefore, Option C is not the correct answer.

Option D: $B(2,-2) \rightarrow B^{\prime}(2,2)$:

Let us translate the coordinate B(2,-2) across y - axis using the translation rule $(x,y)\implies (-x,y)$, we get,

$(2,-2)\implies (-2,-2)$

Thus, we get, $B(2,-2) \rightarrow B^{\prime}(-2,-2)$

Hence, the pair of points $B(2,-2) \rightarrow B^{\prime}(2,2)$ does not has the line of reflection across y - axis.

Therefore, Option D is the correct answer.