Answered

From beginner to expert, IDNLearn.com has answers for everyone. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

Triangle ABC with coordinates [tex]$A(3, -2), B(5, 5), C(-4, 2)$[/tex] is reflected across the x-axis. State the coordinates of the resulting triangle, [tex]A'B'C'[/tex].

Sagot :

GinnyAnsweridn
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].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.