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.

A. Clayton could use the relationship (x,y)\rightarrow (y,x)(x,y)→(y,x) to find the points of the image.

C. C’ will remain in the same location as C because it is on the line of reflection.

D. The image and the pre-image will be congruent triangles.

Step-by-step explanation:

A. Clayton could use the relationship (x,y)\rightarrow (y,x)(x,y)→(y,x) to find the points of the image.

This option is TRUE. When we reflect a shape in the line y=xy=x , we just have to swap the x and y coordinates.

B. .Clayton could negate both the x and y values in the points to find the points of the image.

False; This is a rotation of 180\degree180° about the origin.

C. C’ will remain in the same location as C because it is on the line of reflection.

This statement is True

C’ will move because all points move in a reflection.

This statement is false because,C(2,2) and C'(2,2) will have the same coordinate.

D. The image and the pre-image will be congruent triangles.

This is TRUE because reflection is a shape preserving transformation(rigid motion).

E. The image and pre-image will not have the same orientation because reflections flip figures.

This is False

A. Clayton could use the relationship (x,y)\rightarrow (y,x)(x,y)→(y,x) to find the points of the image.

C. C’ will remain in the same location as C because it is on the line of reflection.

D. The image and the pre-image will be congruent triangles.

Step-by-step explanation:

A. Clayton could use the relationship (x,y)\rightarrow (y,x)(x,y)→(y,x) to find the points of the image.

This option is TRUE. When we reflect a shape in the line y=xy=x , we just have to swap the x and y coordinates.

B. .Clayton could negate both the x and y values in the points to find the points of the image.

False; This is a rotation of 180\degree180° about the origin.

C. C’ will remain in the same location as C because it is on the line of reflection.

This statement is True

C’ will move because all points move in a reflection.

This statement is false because,C(2,2) and C'(2,2) will have the same coordinate.

D. The image and the pre-image will be congruent triangles.

This is TRUE because reflection is a shape preserving transformation(rigid motion).

E. The image and pre-image will not have the same orientation because reflections flip figures.

This is False

Hope this helps :)

Step-by-step explanation:

47 - 90 = 43

43 - 180 = x

x = 137