Reflection Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Reflect the point P(3,−4)P(3, -4) over the x-axis. What are the coordinates of the image?

Solution

  1. 1
    Step 1: Reflecting over the x-axis: the rule is (x,y)→(x,−y)(x, y) \to (x, -y).
  2. 2
    Step 2: Apply to P(3,−4)P(3, -4): P′=(3,−(−4))=(3,4)P' = (3, -(-4)) = (3, 4).
  3. 3
    Step 3: The point flips from below to above the x-axis.

Answer

P′=(3,4)P' = (3, 4)
Reflecting over the x-axis keeps the x-coordinate the same and negates the y-coordinate. The x-axis acts as a mirror: points below the x-axis map to the corresponding points above it, and vice versa.

About Reflection

A rigid transformation that flips a figure over a line (the mirror line), producing a mirror image.

Learn more about Reflection →

More Reflection Examples

Example 2 medium

Reflect the point [formula] over the line [formula]. Find the image.

Example 3 easy

Reflect [formula] over the y-axis. What is the image?

Example 4 hard

Reflect the point [formula] over the line [formula]. Find the image coordinates and explain your met

← All Reflection Examples Reflection Concept

Related Concepts

Geometric Transformation