Question
Your house is located at: A (-2,1); B( 0,1); C(0,3); D(-1,4); E(-2,3)
what are the new points if you reflect the house across the x-axis? is the new house congruent?
what are the new points if you reflect the house across the x-axis? is the new house congruent?
Answers
GPT-4o mini
To reflect points across the x-axis, you keep the x-coordinates the same and change the sign of the y-coordinates.
Let's reflect each point:
1. \( A(-2, 1) \) becomes \( A'(-2, -1) \)
2. \( B(0, 1) \) becomes \( B'(0, -1) \)
3. \( C(0, 3) \) becomes \( C'(0, -3) \)
4. \( D(-1, 4) \) becomes \( D'(-1, -4) \)
5. \( E(-2, 3) \) becomes \( E'(-2, -3) \)
So the new points after reflecting across the x-axis are:
- \( A'(-2, -1) \)
- \( B'(0, -1) \)
- \( C'(0, -3) \)
- \( D'(-1, -4) \)
- \( E'(-2, -3) \)
Now, regarding congruence: Two shapes are congruent if they have the same size and shape, even if they are oriented differently. The reflected points maintain the same distances and angles relative to one another as the original points. Thus, the new house after reflection is congruent to the original house.
Let's reflect each point:
1. \( A(-2, 1) \) becomes \( A'(-2, -1) \)
2. \( B(0, 1) \) becomes \( B'(0, -1) \)
3. \( C(0, 3) \) becomes \( C'(0, -3) \)
4. \( D(-1, 4) \) becomes \( D'(-1, -4) \)
5. \( E(-2, 3) \) becomes \( E'(-2, -3) \)
So the new points after reflecting across the x-axis are:
- \( A'(-2, -1) \)
- \( B'(0, -1) \)
- \( C'(0, -3) \)
- \( D'(-1, -4) \)
- \( E'(-2, -3) \)
Now, regarding congruence: Two shapes are congruent if they have the same size and shape, even if they are oriented differently. The reflected points maintain the same distances and angles relative to one another as the original points. Thus, the new house after reflection is congruent to the original house.