Reflection Reflection B A A Line of Reflection
Reflection
Reflection B A
A Line of Reflection B C
A B C
Line of reflection A A’ image Pre-image B C C’ B’
line of reflection / perpendicular bisector A D A’ image Pre-image B C C’ B’
line of reflection / perpendicular bisector A D A’ image Pre-image E B C C’ B’
AD = DA’ BE = EB’ CE = EC’ line of reflection / perpendicular bisector A D A’ image Pre-image E B C C’ B’
• A reflection is a transformation across a line, called the line of reflection, so that the line of reflection is the perpendicular bisector of each segment joining each point and its image. • A reflection is an isometry, so the image is always congruent to the pre-image.
• Iso which means equal and metry which means measurement. • Isometry means equal measurement
P Q O
P O Q
A
B A
Assessment • 1. If a transformation is an isometry, how would you describe the relationship between the preimage and the image? • 2. Copy the figure and the line of reflection. Draw the reflection of the figure across the line.
Reflections in the Coordinate Plane • Across the x-axis y P(x, y) x P’(x, – y) • (x, y) (x, – y)
Reflections in the Coordinate Plane • Across the y-axis y P’(– x , y) P(x, y) x • (x, y) (– x, y)
Reflections in the Coordinate Plane Across the line y = x P(x, y) P’(y, x) y=x • (x, y) (y, x)
Reflections in the Coordinate Plane • Example: • Reflect the figure with the given vertices M(1, 2), N(1, 4), P(3, 3) across the y-axis. M(1, 2) M’(– 1, 2) N(1, 4) N’(– 1, 4) P(3, 3) P’(– 3, 3) Click here twice to see answer
Reflections in the Coordinate Plane • Copy and complete the graphic organizer. Line of Reflection x-axis Image of (a, b) Example (a, - b) (1, 2) (1, -2) y-axis (- a, b) (1, 2) ( -1, 2) y=x (b, a) (1, 2) (2, 1) Answers
Homework • Page 827 • # 1 - 12
- Slides: 35