9000149308
Level:
B
Consider a rotation through an angle either
\(\alpha = 180^{\circ }\) or
\(\alpha = 360^{\circ }\). How
many lines which are mapped into itself exists for this rotation?
infinitely many
none
one
two
Transformations
9000149309
Level:
C
Consider a dilatation which maps \(A\)
onto \(B\). The center is
the dilatation is \(S\).
Find a correct statement.
The point \(S\) is on the
line through the points \(A\)
and \(B\).
The points \(S\),
\(A\) and
\(B\) form a right
triangle \(ABS\).
The distance from \(S\)
to \(A\) is smaller than
the distance from \(A\)
to \(B\).
The points \(S\),
\(A\) and
\(B\) form a
triangle \(ABS\)
with at least two sides of equal length.
9000149305
Level:
B
Given a translation \(T\)
of a plane, find the lines which are mapped to the same line by
\(T\).
All lines parallel to the translation vector are mapped into itself.
All lines perpendicular to the translation vector are mapped into itself.
There are no lines which are mapped into itself by the translation.
Every line is mapped into itself by the translation.
9000149304
Level:
A
How many points of symmetry there exist for a rhombus? A rhombus -- opposite sides are parallel and all sides have equal length. (A point is a point of
symmetry of the rhombus if the reflection through this point maps the rhombus into
itself.)
one
none
two
four
9000149301
Level:
A
Which of the following is true for a reflection through a line?
It is a congruent mapping (preserves shapes and dimensions).
It is a similar mapping (preserves shapes, may change dimensions and position).
It is an identity mapping (objects are mapped to itself).
9000149302
Level:
A
Given a line in a plane, find how many points are mapped onto itself with reflection
through this line.
infinitely many
none
one
two
9000149310
Level:
C
The dilatation defined by a center and a scale factor
\(k = -1\) is
equivalent to another geometric mapping. Which one?
reflection through the point
translation
reflection through the line
rotation
9000149303
Level:
A
Which of the following answers contains three letters with point symmetry? (A letter
has a point of symmetry if there exists a point, such that the reflection through this
point maps the letter into itself.)
O, N, Z
A, M, O
A, O, B
H, O, U
9000149306
Level:
B
Given a translation of a plane, find the property of a line obtained by translating a line
\(r\). The
line \(r\) is
neither parallel not perpendicular to the translation vector.
The resulting line is parallel to the line
\(r\).
The resulting line is perpendicular to the translation vector.
The resulting line is perpendicular to the line
\(r\).
The resulting line is the line \(r\).
(The line \(r\)
is mapped into itself.)
9000149307
Level:
B
The rotation through an angle \(\alpha = 180^{\circ }\)
is equivalent to some other geometric mapping. Which one?
reflection through the point
reflection through the line
translation