Question

Trapezoid ABCD is reflected over the line y = x. What rule shows the input and output of the reflection, and what is the new coordinate of A'?

A) (x,y) → (y,x); A' is at (1, -5)
B) (x,y) → (y-x); A' is at (1, 5)
C) (x,y) → (-x,y); A' is at (5, 1)
D) (x,y) → (-x-y); A' is at (5, -1)

Answer 1

The correct reflection rule over the line y = x is (x, y) → (y, x) and the new coordinates of point A' are (1, -5).

Step-by-step explanation:

When a trapezoid ABCD is reflected over the line y = x, the rule that represents the input (original coordinates) to the output (reflected coordinates) is (x, y) → (y, x). This rule swaps the x-coordinate with the y-coordinate for each point on the trapezoid. Hence, the correct option that shows both the rule and the new coordinate of A' is option A: (x, y) → (y, x); A' is at (1, -5). This means that if point A had coordinates (x, y), the reflected point A' will now have coordinates (y, x). For instance, if A had coordinates (-5, 1), reflecting A over the line y = x would give A' coordinates (1, -5).