Solved Examples

Problem 1: Alphabet Symmetry

Question: Which capital letters of the English alphabet have:

1. Reflection symmetry (vertical)?
2. Reflection symmetry (horizontal)?
3. No reflection symmetry?

Solution:

1. Vertical Line: A, H, I, M, O, T, U, V, W, X, Y.
2. Horizontal Line: B, C, D, E, H, I, K, O, X.
3. No Line: F, G, J, L, N, P, Q, R, S, Z.

Problem 2: Rotational Calculation

Question: A figure has an angle of symmetry of $40^{\circ}$.

1. What is the order of rotational symmetry?
2. List all the angles of rotation.

Solution:

1. Order: $\frac{360^{\circ}}{40^{\circ}} = 9$.
2. Angles: Just keep adding $40^{\circ}$ until you reach $360^{\circ}$. $40^{\circ}, 80^{\circ}, 120^{\circ}, 160^{\circ}, 200^{\circ}, 240^{\circ}, 280^{\circ}, 320^{\circ}, 360^{\circ}$

Problem 3: The Mirror Game

Question: An object is placed at point $(2, 3)$ on a grid. A mirror is placed on the x-axis (the horizontal line $y=0$). Where will the image appear?

Solution: When reflecting over a horizontal line:

• The x-coordinate stays the same.
• The distance from the mirror stays the same, but on the opposite side.
• Point is 3 units above the axis. Image will be 3 units below.
• Image Coordinates: $(2, -3)$.