1103162505
Level:
B
The triangle \( ABC \) is translated by the vector \( \vec{u} \) (see the picture). Which of the following pictures shows correctly the image \( A'B'C' \) of the triangle \( ABC \) in the given translation?
Geometric mappings
2110016701
Level:
B
Let \(ABCD\) be a rectangle where \(|AB|=2|BC|\) and let \(S\) be a point on the perpendicular bisector of the side \(BC\) such that its distance from \(BC\) is \(\frac12|BC|\) (see the picture). The rectangle \(ABCD\) rotates \(90^{\circ}\) clockwise about \(S\). Which of the pictures shows the rectangle \(A'B'C'D'\) that is the image of rotated rectangle \(ABCD\)?
2110016702
Level:
B
An equilateral triangle \( ABC \) rotates \( 90^{\circ} \) clockwise about the point \( O(4;2) \). Which of the pictures shows the triangle \( A'B'C' \) that is the image of the rotated triangle \( ABC \)?
2110016703
Level:
B
Let a rectangle \( ABCD \) be translated by vector \( \overrightarrow{AS} \), where \( S \) is the center of the rectangle. Which of the following pictures shows correctly the image \( A'B'C'D' \) of the rectangle \( ABCD \) in described translation?
2110016704
Level:
B
The triangle \( ABC \) is translated by the vector \( \vec{u} \) (see the picture). Which of the following pictures shows correctly the image \( A'B'C' \) of the triangle \( ABC \) in the given translation?
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.
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
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
1103162601
Level:
C
Let \( ABCD \) be a square. Find the dilated image of the square with \( A \) being the centre of dilation and the scale factor \( \frac12 \) (see the picture).
