10 questions · Form 2 Mathematics Bab 7: Isometric Transformations
Two geometric figures are congruent if they have:
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Two geometric figures are congruent if they have:
Answer: A
Congruence requires both identical geometric shape and identical physical size.
2. Under a rotation of 270° clockwise about origin, point (2, 3) is mapped to:
Answer: A
270° clockwise rotation is equivalent to 90° counterclockwise rotation, mapping (x, y) -> (-y, x). So (2, 3) becomes (-3, 2).
3. What is the image of point B(4, -3) when reflected in the x-axis?
Answer: A
Reflection in the x-axis keeps the x-coordinate same and negates the y-coordinate: (x, y) -> (x, -y), so (4, -3) becomes (4, 3).
4. Find the image of point F(1, 5) under a 90° clockwise rotation about the origin O(0,0).
Answer: A
A 90° clockwise rotation about origin maps (x, y) -> (y, -x). Thus, (1, 5) becomes (5, -1).
5. Find the image of point A(3, 5) under the translation vector (2, -4)^T.
Answer: A
x' = 3 + 2 = 5; y' = 5 + (-4) = 1. The image is A'(5, 1).
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. 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).
8. 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°.
9. 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.
10. What are the coordinates of point E(3, 4) after a rotation of 180° about the origin O(0,0)?
Answer: A
A 180° rotation about the origin changes (x, y) to (-x, -y), giving E'(-3, -4).