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On a coordinate plane, a 5-sided figure has points A prime (negative 4, negative 2), B prime (negative 4, 4), C prime (6, 4), D prime (8, 1), and E prime (6, negative 2).

Figure ABCDE was reflected across the line y = x to create figure A'B'C'D'E'. What are the coordinates of the pre-image of E'?



E(
,
)

1 answer

To find the pre-image of the point E' after reflecting across the line \( y = x \), you can use the rule for reflection over the line \( y = x \). The coordinates of a point \( (x, y) \) after reflection over this line become \( (y, x) \).

Given the coordinates of \( E' \) are \( (6, -2) \):

  • The x-coordinate of the pre-image \( E \) will be the y-coordinate of \( E' \), which is \( -2 \).
  • The y-coordinate of the pre-image \( E \) will be the x-coordinate of \( E' \), which is \( 6 \).

Thus, the coordinates of the pre-image \( E \) are \( (-2, 6) \).

So, \( E(-2, 6) \).