Answered

Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Get comprehensive answers to all your questions from our network of experienced experts.

Transformations: Reflections

Triangle [tex]A B C[/tex] has coordinates [tex]A(1,-1), B(0,2)[/tex], and [tex]C(2,1)[/tex] and it is reflected over the line [tex]y=-x[/tex] to form triangle [tex]A^{\prime} B^{\prime} C^{\prime}[/tex]. What are the coordinates of triangle [tex]A^{\prime} B^{\prime} C^{\prime}[/tex]?

Sagot :

GinnyAnsweridn
To find the coordinates of the reflected triangle [tex]\( A'B'C' \)[/tex], we need to reflect each vertex of the original triangle [tex]\( ABC \)[/tex] over the line [tex]\( y = -x \)[/tex].

When reflecting a point [tex]\((x, y)\)[/tex] over the line [tex]\( y = -x \)[/tex], the coordinates of the reflected point [tex]\((x', y')\)[/tex] can be found by swapping the coordinates and negating them:
[tex]\[ (x', y') = (-y, -x) \][/tex]

Let's apply this transformation to each vertex of the triangle one by one:

Step-by-step Solution:

1. Reflect point [tex]\( A(1, -1) \)[/tex]:
- Original coordinates: [tex]\( (1, -1) \)[/tex]
- Swap and negate: [tex]\( (-(-1), -1) = (1, -1) \)[/tex]
- So, [tex]\( A' = (1, -1) \)[/tex]

2. Reflect point [tex]\( B(0, 2) \)[/tex]:
- Original coordinates: [tex]\( (0, 2) \)[/tex]
- Swap and negate: [tex]\( (-2, -0) = (-2, 0) \)[/tex]
- So, [tex]\( B' = (-2, 0) \)[/tex]

3. Reflect point [tex]\( C(2, 1) \)[/tex]:
- Original coordinates: [tex]\( (2, 1) \)[/tex]
- Swap and negate: [tex]\( (-1, -2) = (-1, -2) \)[/tex]
- So, [tex]\( C' = (-1, -2) \)[/tex]

Therefore, the coordinates of the reflected triangle [tex]\( A'B'C' \)[/tex] are:
[tex]\[ A'(1, -1), B'(-2, 0), C'(-1, -2) \][/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.