To find the reflected coordinates of triangle [tex]\(ABC\)[/tex] across the x-axis, follow these steps:
1. Understand Reflection Across the x-axis:
When reflecting a point over the x-axis, the x-coordinate remains the same while the y-coordinate changes its sign. Mathematically, if you have a point [tex]\((x, y)\)[/tex], its reflection across the x-axis will be [tex]\((x, -y)\)[/tex].
2. Apply Reflection to Each Point:
- Point A: Given coordinates are [tex]\((3, -2)\)[/tex]. The x-coordinate does not change, and the y-coordinate changes sign.
- Thus, [tex]\(A' = (3, -(-2)) = (3, 2)\)[/tex].
- Point B: Given coordinates are [tex]\((5, 5)\)[/tex]. The x-coordinate does not change, and the y-coordinate changes sign.
- Thus, [tex]\(B' = (5, -(5)) = (5, -5)\)[/tex].
- Point C: Given coordinates are [tex]\((-4, 2)\)[/tex]. The x-coordinate does not change, and the y-coordinate changes sign.
- Thus, [tex]\(C' = (-4, -(2)) = (-4, -2)\)[/tex].
3. State the New Coordinates:
- The coordinates of the reflected triangle [tex]\(A'B'C'\)[/tex] are:
- [tex]\(A' = (3, 2)\)[/tex]
- [tex]\(B' = (5, -5)\)[/tex]
- [tex]\(C' = (-4, -2)\)[/tex]
Therefore, the coordinates of triangle [tex]\(A'B'C'\)[/tex] after reflecting triangle [tex]\(ABC\)[/tex] across the x-axis are [tex]\((3, 2)\)[/tex], [tex]\((5, -5)\)[/tex], and [tex]\((-4, -2)\)[/tex].
