Geometric Transformations and Properties Quiz

Explore geometric transformations: reflections, rotations, dilations, and their effects. Test your knowledge with 12 questions on shape preservation, matrix operations, and more.

Practice Learn Test

Which transformation does not preserve the shape and size of an object?

Translation

Rotation

Reflection

Dilation

What is the sum of the interior angles of a triangle?

90 degrees

180 degrees

360 degrees

270 degrees

Which property is not preserved under a rotation transformation?

Angle measures

Parallelism

Line segment length

Orientation

What is the result of reflecting the point (3, 4) across the y-axis?

(-3, -4)

(-3, 4)

(3, -4)

(4, 3)

In a 45-45-90 right triangle, if the length of one leg is 8, what is the length of the hypotenuse?

8√2

4√2

Which matrix represents a reflection over the x-axis?

[[1, 0], [0, -1]]

[[0, 1], [1, 0]]

[[-1, 0], [0, 1]]

[[1, 0], [0, 1]]

A square has vertices at (1,1), (1,-1), (-1,-1), and (-1,1). After a dilation with a scale factor of 3 centered at the origin, what are the coordinates of the new vertices?

(3,3), (3,-3), (-3,-3), (-3,3)

(2,2), (2,-2), (-2,-2), (-2,2)

(4,4), (4,-4), (-4,-4), (-4,4)

(1,1), (1,-1), (-1,-1), (-1,1)

Which figure is always created by a composition of a reflection over the x-axis followed by a reflection over the y-axis?

Circle

Rectangle

Triangle

The same figure rotated 180 degrees

If a shape undergoes a dilation centered at the origin with a scale factor of 2, what happens to the coordinates of any point (x, y) on the shape?

(x/2, y/2)

(2x, 2y)

(-x, -y)

(x^2, y^2)

#10

What is the formula to find the area of a circle after a dilation with a scale factor of 'k'?

πr^2

kπr^2

π(kr)^2

k^2πr^2

#11

In an affine transformation represented by the matrix [[a, b], [c, d]] acting on a point (x, y), how do you calculate the transformed x-coordinate?

ax + by

ax + cy

dx + by

bx + ay

#12

In a tessellation, what is the significance of the angle measures of the shapes involved?

They determine the type of symmetry.

They must sum to 180 degrees for any two adjacent shapes.

They determine how many of each shape can meet at a vertex.

They are irrelevant as long as the shapes fit together without gaps.