Question

The values on both axes range from negative 10 to 10 in one-unit increments. The coordinates of the vertices of the rectangle are as follows: upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis 6 comma 5 right parenthesis, upper C is left parenthesis 6 comma negative 1 right parenthesis, and upper D is left parenthesis negative 4 comma negative 1 right parenthesis.


Image Long DescriptionThe values on both axes range from negative 10 to 10 in one-unit increments. The coordinates of the vertices of the rectangle are as follows: upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis 6 comma 5 right parenthesis, upper C is left parenthesis 6 comma negative 1 right parenthesis, and upper D is left parenthesis negative 4 comma negative 1 right parenthesis.

Complete the equations identifying both lines of reflection that will flip the given figure onto itself.

Answer 1

The rectangle's center is at the midpoint of A and C: ((-4+6)/2, (5+(-1))/2) = (1, 2). The two lines of symmetry are the vertical and horizontal lines through that center:

x = 1 and y = 2.

(Reflection across x = 1 swaps A ↔ B and D ↔ C; reflection across y = 2 swaps A ↔ D and B ↔ C.)