Identify the reflection rule on a coordinate plane that verifies that triangle A(-1,7), B(6,5), C(-2,2) and A'(-1,-7), B'(6,-5), C'(-2,-2) triangle are congruent when reflected over the x-axis?

A) (x, y) → (-x, -y)
B) (x, y) → (x, -y)
C) (x, y) → (-x, y)
D) the triangles are not congruent

Question

A) (x, y) → (-x, -y)
B) (x, y) → (x, -y)
C) (x, y) → (-x, y)
D) the triangles are not congruent

Ella Armstrong · Accepted Answer

It follows the rule #color(green)((B) -> (x, -y))#

Since the triangle is reflected on x axis, onlyy coordinates will get changed from the current sign to the opposite (i.e.. #+ to -, or - to +)#. But the #x# coordinates will remain the same.

Sadie Adams · Answer

undefined The reflection rule on a coordinate plane that verifies the congruence of triangle ABC and its reflection over the x-axis (A'B'C') is that the corresponding vertices have the same x-coordinates and the y-coordinates of each vertex are negated.

HIX Tutor · Answer

undefined To show that triangle A, B, C and triangle A', B', C' are congruent when reflected over the x-axis, follow these steps:

1. **Understand Reflection**: When you reflect a point over the x-axis, the x-coordinate stays the same, and the y-coordinate changes sign.

2. **Reflect Points A, B, and C**:
   - Point A(-1, 7) reflects to A'(-1, -7).
   - Point B(6, 5) reflects to B'(6, -5).
   - Point C(-2, 2) reflects to C'(-2, -2).

3. **Check Each Point**:
   - For A: The reflection from (−1, 7) to (−1, −7) is correct.
   - For B: The reflection from (6, 5) to (6, −5) is correct.
   - For C: The reflection from (−2, 2) to (−2, −2) is correct.

4. **Conclusion**: Since each point A, B, and C reflects correctly to A', B', and C', the triangles are congruent by reflection over the x-axis.

So, the reflection rule is: **Reflect over the x-axis by changing the sign of the y-coordinate.**

Identify the reflection rule on a coordinate plane that verifies that triangle A(-1,7), B(6,5), C(-2,2) and A'(-1,-7), B'(6,-5), C'(-2,-2) triangle are congruent when reflected over the x-axis?

A) (x, y) → (-x, -y) B) (x, y) → (x, -y) C) (x, y) → (-x, y) D) the triangles are not congruent

A) (x, y) → (-x, -y)
B) (x, y) → (x, -y)
C) (x, y) → (-x, y)
D) the triangles are not congruent