Transformation Geometry: All Four Transformations — Worksheet & Memo

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Grade 8 · Transformation Geometry

Transformation Geometry: All Four Transformations

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Reflect (2 ; 7) in the y-axis. (reflect)
(1)
(−2 ; 7)✓ (1)
2
Reflect (4 ; −1) in the x-axis. (reflect)
(1)
(4 ; 1)✓ (1)
3
Reflect (5 ; 2) in the line y = x. (reflect)
(1)
(2 ; 5)✓ (1)
4
Reflect (−3 ; 6) in the y-axis. (reflect)
(1)
(3 ; 6)✓ (1)
5
Translate (1 ; 4) by 5 right and 2 up. (translate)
(1)
(1 + 5 ; 4 + 2) = (6 ; 6)✓ (1)
6
Translate (3 ; −2) by 2 left and 3 up. (translate)
(1)
(3 − 2 ; −2 + 3) = (1 ; 1)✓ (1)
7
Rotate (2 ; 5) by 180° about the origin. (rotate)
(1)
(−2 ; −5)✓ (1)
8
Rotate (−4 ; 1) by 180° about the origin. (rotate)
(1)
(4 ; −1)✓ (1)
9
Enlarge (3 ; 4) by scale factor 2 from the origin. (enlarge)
(1)
(6 ; 8)✓ (1)
10
Enlarge (4 ; 6) by scale factor 1/2 from the origin. (reduce)
(2)
(2 ; 3)✓✓ (2)
11
Write down the number of lines of symmetry of a square, a rectangle and a parallelogram.
(3)
Square 4 ✓; rectangle 2 ✓; parallelogram 0 ✓(3)
12
Explain why a diagonal of a rectangle is NOT a line of symmetry.
(2)
Folding along the diagonal does not make the two halves coincide ✓ — the halves are congruent but do not land on top of each other, unless the rectangle is a square ✓(2)
13
How many lines of symmetry does a regular hexagon have, and how many does an isosceles triangle have?
(2)
Regular hexagon 6 ✓; isosceles triangle 1 ✓(2)
14
A parallelogram has no lines of symmetry but still looks balanced. Explain.
(2)
It has rotational symmetry — turning it 180° about its centre maps it onto itself ✓ — but there is no line it can be folded along so the halves match ✓(2)

TOTAL: 20 marks