10 questions · Form 2 Mathematics Bab 7: Isometric Transformations
What is the order of rotational symmetry of a regular hexagon?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the order of rotational symmetry of a regular hexagon?
Answer: A
A regular n-gon has an order of rotational symmetry equal to n. For a hexagon, n = 6.
2. What is the result of reflecting a point (x, y) twice across the same line of reflection?
Answer: A
Reflecting a point twice across the same axis returns it to its original position (x, y).
3. A point M(4, -2) is reflected in line x = 3. What are the coordinates of its image M'?
Answer: A
Distance from x = 4 to x = 3 is 1 unit left. The image lies 1 unit left of x = 3, which is x = 2. So M' is (2, -2).
4. Find the image of point G(-3, 4) under a 90° counterclockwise rotation about origin O(0,0).
Answer: A
A 90° counterclockwise rotation maps (x, y) -> (-y, x). So (-3, 4) becomes (-4, -3).
5. Point P(-2, 7) is mapped to P'(3, 2) under a translation. Find the translation vector.
Answer: A
a = 3 - (-2) = 5; b = 2 - 7 = -5. The translation vector is (5, -5)^T.
6. Find the image of point D(2, 6) under a reflection in the line y = x.
Answer: A
Reflection in line y = x swaps x and y coordinates: (x, y) -> (y, x), so (2, 6) becomes (6, 2).
7. Which of the following is NOT an isometric transformation?
Answer: A
An isometry preserves shape and size. Enlargement changes the size of the object, so it is not an isometry.
8. Find the image of (0, -4) under a translation (3, 4)^T.
Answer: A
x' = 0 + 3 = 3; y' = -4 + 4 = 0. Image is (3, 0).
9. If the image of point K(x, y) under translation (-3, 5)^T is K'(2, 1), find the original coordinates of K.
Answer: A
x - 3 = 2 => x = 5; y + 5 = 1 => y = -4. Thus, K is (5, -4).
10. Calculate the angle of rotation for a regular pentagon to fit onto itself in one step.
Answer: A
Angle of rotation = 360° / order of symmetry = 360° / 5 = 72°.