Question

Clayton needs to reflect the triangle below across the line y = x.

On a coordinate plane, triangle A B C has points (5.5, 7), (6, 2), (4, 4).

Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.

Answer 1

True:
- Clayton could use (x, y) → (y, x) to find the image. (Reflection across y = x swaps coordinates.)
- C’ will remain in the same location as C because C = (4,4) lies on the line y = x.
- The image and the pre-image will be congruent triangles. (Reflections are isometries.)
- The image and pre-image will not have the same orientation because reflections reverse orientation.

False:
- Negating both x and y (→ (−x, −y)) is not the reflection across y = x. (That is a 180° rotation about the origin.)
- “C’ will move because all points move in a reflection” is false — points on the line of reflection stay fixed.

(For reference, A' = (7, 5.5), B' = (2, 6), C' = (4, 4).)