$$ riangle Q R S $$ contains the $$ -: Q(4,2), R(5,1) $$, and $$ S(3,7) $$. If the $$ \Delta $$ is reflected across the $$ y $$-axis, what will $$ S^{\prime} $$ be? Select one: a. $$ S^{\prime}(3,7) $$ b. $$ S^{\prime}(3,7) $$ c. $$ S^{\prime}(-3,7) $$ d. $$ S^{\prime}(-3,-7) $$

Question

$$ 	riangle Q R S $$ contains the $$ -: Q(4,2), R(5,1) $$, and $$ S(3,7) $$. If the $$ \Delta $$ is reflected across the $$ y $$-axis, what will $$ S^{\prime} $$ be? Select one: a. $$ S^{\prime}(3,7) $$ b. $$ S^{\prime}(3,7) $$ c. $$ S^{\prime}(-3,7) $$ d. $$ S^{\prime}(-3,-7) $$

UpStudy AI · Accepted Answer

To find the coordinates of point $$ S' $$ after reflecting point $$ S(3,7) $$ across the $$ y $$-axis, we follow these steps:

1. **Understanding Reflection Across the $$ y $$-Axis**: 
   - When a point $$ (x, y) $$ is reflected across the $$ y $$-axis, its $$ x $$-coordinate changes sign while the $$ y $$-coordinate remains the same. 
   - Therefore, the reflection of point $$ S(3, 7) $$ will be $$ S'(-x, y) $$.

2. **Applying the Reflection**:
   - For point $$ S(3, 7) $$:
     - The $$ x $$-coordinate is $$ 3 $$, so after reflection, it becomes $$ -3 $$.
     - The $$ y $$-coordinate remains $$ 7 $$.

3. **Resulting Coordinates**:
   - Thus, the coordinates of $$ S' $$ after reflection are $$ S'(-3, 7) $$.

Now, let's check the options provided:

- a. $$ S^{\prime}(3,7) $$
- b. $$ S^{\prime}(3,7) $$
- c. $$ S^{\prime}(-3,7) $$
- d. $$ S^{\prime}(-3,-7) $$

The correct answer is:
**c. $$ S^{\prime}(-3,7) $$**.
$$ S' $$ is at $$ (-3, 7) $$.

\( \triangle Q R S \) contains the \( -: Q(4,2), R(5,1) \), and \( S(3,7) \). If the \( \Delta \) is reflected across the \( y \)-axis, what will \( S^{\prime} \) be? Select one: a. \( S^{\prime}(3,7) \) b. \( S^{\prime}(3,7) \) c. \( S^{\prime}(-3,7) \) d. \( S^{\prime}(-3,-7) \)

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