Question

Predict what will happen to the coordinates of a point (x, y) as the point reflects across a line to produce point (x', y'). Choose the x-axis, y-axis, y = x and y = -x for the lines of reflection. Express your answers in terms of x and y. (Be sure to watch your signs.)

Answer 1

• x-axis: (x, y) ⇒ (x, -y)
• y-axis: (x, y) ⇒ (-x, y)
• y = x: (x, y) ⇒ (y, x)
• y = -x: (x, y) ⇒ (-y, -x)

Explanation:

The attached diagram may be helpful. In the diagram, each reflected point is connected to the original by a line segment perpendicular to the line of reflection.

Reflection across the x-axis

(3, 1) ⇒ (3, -1)

(x, y) ⇒ (x, -y)

Reflection across the y-axis

(3, 1) ⇒ (-3, 1)

(x, y) ⇒ (-x, y)

Reflection across y = x

(3, 1) ⇒ (1, 3)

(x, y) ⇒ (y, x)

Reflection across y = -x

(3, 1) ⇒ (-1, -3)

(x, y) ⇒ (-y, -x)