Reflect shapes across x-axis and y-axis. Understand how coordinates change during reflection and create accurate mirror images.
Click on each step to explore reflection in axes:
Identify which axis is the mirror line - either the x-axis (horizontal) or y-axis (vertical). This line acts like a perfect mirror.
Use the coordinate transformation rules to find where each point moves after reflection.
Calculate the new coordinates for each vertex and plot them accurately on your coordinate grid.
Connect the reflected points to form the mirror image and verify it matches the original shape exactly.
Reflection in axes creates perfect mirror images of shapes across the x-axis or y-axis, maintaining size and shape while changing position.
Click on the grid to plot points, then see them reflect across different axes!
(x, y) → (x, -y)
Keep x-coordinate, change sign of y-coordinate
(-x, y) ← (x, y)
Change sign of x-coordinate, keep y-coordinate
Reflection creates symmetrical patterns in art, architecture, and graphic design. Many beautiful designs use reflection symmetry.
Engineers use reflection to design symmetrical structures like bridges, buildings, and mechanical parts that need to be balanced.
Video games and animations use reflection algorithms to render realistic water reflections and mirror effects.
Original: A(2, 3), B(5, 1), C(1, 1)
Apply rule (x, y) → (x, -y):
A(2, 3) → A'(2, -3)
B(5, 1) → B'(5, -1)
C(1, 1) → C'(1, -1)
Result: Triangle flipped below x-axis
The reflected triangle is the same size and shape, just upside down!
Original: P(1, 2), Q(4, 2), R(4, 5), S(1, 5)
Apply rule (x, y) → (-x, y):
P(1, 2) → P'(-1, 2)
Q(4, 2) → Q'(-4, 2)
R(4, 5) → R'(-4, 5)
S(1, 5) → S'(-1, 5)
Result: Rectangle flipped to the left side of y-axis
Width and height remain exactly the same!
Special Case: What happens to points on the mirror line?
Point on x-axis: (3, 0) → (3, 0)
Point on y-axis: (0, -2) → (0, -2)
They don't move!
Why? Points on the mirror line are their own reflection
Like standing directly in front of a mirror - you don't see yourself move sideways!
Problem: Applying the wrong reflection rule and changing the wrong coordinate.
Wrong: (3, 2) in x-axis → (-3, 2) ❌
Right: (3, 2) in x-axis → (3, -2) ✅
Solution: X-axis reflection changes y-coordinate, Y-axis reflection changes x-coordinate.
Problem: Moving the point but not changing positive to negative (or vice versa).
Wrong: (-4, 3) in y-axis → (4, 3) should be (-4, 3) ❌
Right: (-4, 3) in y-axis → (4, 3) ✅
Solution: Always change the sign of the coordinate that's being reflected.
Problem: Thinking that points on the mirror line move when they should stay put.
Wrong: (0, 5) in y-axis → (5, 0) ❌
Right: (0, 5) in y-axis → (0, 5) ✅
Solution: Points on the mirror line are their own reflection - they don't move!
You have mastered reflection in axes! Here's what you can now do:
Use coordinate transformation rules to reflect shapes across x-axis and y-axis
Transform coordinate points accurately using (x,y) → (x,-y) and (x,y) → (-x,y)
Draw precise reflections that maintain shape and size while changing position
Check that reflected shapes are equidistant from the mirror line
You've mastered reflection in axes
You can now create perfect mirror images and understand how coordinates change during reflection!
Ready for more complex reflections? In Chapter 8.5, you'll learn to reflect shapes in diagonal lines and other mirror lines beyond just the axes!