Symmetry and geometric transformations

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 \(ABCD\)?

Symmetry and geometric transformations

2010016709

2010016710

2110016708

2110016707

2110016706

2110016705

2110016704

2110016703

2110016702

2110016701

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