The vertices of \( \triangle A B C \) are \( A(-4,1), B(-1,5) \), and \( C(2,4) \). The triangle is reflected over the \( x \)-axis. Use arre notation to describe the original triangle and its reflection. a. \( A(-4,1), B(-1,5), C(2,4) \rightarrow A^{\prime}(-4,1), B^{\prime}(-1,5), C^{\prime}(2,4) \) b. \( A(-4,1), B(-1,5), C(2,4) \rightarrow A^{\prime}(-4,-1), B^{\prime}(-1,-5), C^{\prime}(2,-4) \) c. \( A(-4,1), B(-1,5), C(2,4) \rightarrow A^{\prime}(4,1), B^{\prime}(1,5), C^{\prime}(-2,4) \) d. \( A(-4,1), B(-1,5), C(2,4) \rightarrow A^{\prime}(4,-1), B^{\prime}(1,-5), C^{\prime}(-2,-4) \)

When reflecting points over the \( x \)-axis, the \( y \)-coordinates of the points change signs while the \( x \)-coordinates remain the same. For your triangle \( \triangle ABC \), the vertices are \( A(-4, 1) \), \( B(-1, 5) \), and \( C(2, 4) \). After reflecting over the \( x \)-axis, the coordinates become: - \( A'(-4, -1) \) - \( B'(-1, -5) \) - \( C'(2, -4) \) Thus, the correct notation to describe the original triangle and its reflection is: b. \( A(-4,1), B(-1,5), C(2,4) \rightarrow A^{\prime}(-4,-1), B^{\prime}(-1,-5), C^{\prime}(2,-4) \). Reflecting a triangle is a great way to explore symmetry in geometry! This change creates a mirror image across the \( x \)-axis, and it's fascinating to see how the positions flip while maintaining the same shape and size, showcasing the principles of congruence. If you love transformations, diving into the world of transformations can be extremely rewarding! Try experimenting with other types of reflections, such as over the \( y \)-axis or even rotations, to see how they affect the positions of points in your triangle! Exploring these concepts can lead to a deeper understanding of geometric properties and relationships.