Answer:
Clayton could use the relationship (x,y)→ (y,x) to find the points of the image
C’ will remain in the same location as C because it is on the line of 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
Explanation:
Verify each statement
case A) Clayton could use the relationship (x,y)→ (y,x) to find the points of the image
The statement is true
we know that
The rule of the reflection of a point across the line y=x is equal to
(x,y)→ (y,x)
case B) Clayton could negate both the x and y values in the points to find the points of the image
The statement is false
case C) C’ will remain in the same location as C because it is on the line of reflection
The statement is true
If a point is on the line of reflection (y=x), then the point remain in the same location because the x and y coordinates are equal
case D) C’ will move because all points move in a reflection
The statement is false
Because C' is on the line of reflection (y=x), then the point remain in the same location
case E) The image and the pre-image will be congruent triangles
The statement is true
Because the reflection not change the length sides of the triangle or the measure of its internal angles. Reflection changes only the orientation of the figure
case F) The image and pre-image will not have the same orientation because reflections flip figures
The statement is true
Because in a reflection across the line y=x, the x coordinate of the pre-image becomes the y-coordinate of the image and the y-coordinate of the pre-image becomes the x-coordinate of the image