Geometric mappings
Homothety of Two Objects
Submitted by michaela.bailova on Tue, 12/17/2024 - 16:092010016709
Level:
A
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:
A
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:
C
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:
C
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:
C
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:
C
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:
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?
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?
