Geometric mappings

2010016709

Level:

Which of the following answers contains three letters so that each letter is without a point of 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.)

A, U, K

S, O, H

N, U, K

A, O, H

2010016710

Level:

How many points of symmetry there exist for an equilateral triangle? (A point is the point of symmetry of a triangle if the reflection through this point maps the triangle into itself.)

none

one

two

three

2110016708

Level:

Let \(ABC\) be a triangle (see the picture). Find the dilated image of the triangle with \( O \) (the origin) being the centre of dilation and the scale factor \( -2 \).

2110016707

Level:

Let \( ABC\) be a triangle with the centroid \( T \) (see the picture). Find the dilated image of the triangle with \( T \) being the centre of dilation and the scale factor \( \frac12 \).

2110016706

Level:

Let \( ABC \) be a triangle (see the picture). Find the dilated image of the triangle with \( B \) being the centre of dilation and the scale factor \( \frac32 \).

2110016705

Level:

Let \( ABCD \) be a square. Find the dilated image of the square with \( S \) being the centre of dilation and scale factor \( \frac12 \). The point \( S \) is also the middle of the square \( ABCD \) (see the picture).

2110016704

Level:

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?

2110016703

Level:

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?

2110016702

Level:

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 \( ABC \)?

2110016701

Level:

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 \(ABCD\)?

2010016709

2010016710

2110016708

2110016707

2110016706

2110016705

2110016704

2110016703

2110016702

2110016701

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