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Geometric Transformations and Properties Quiz

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

Dilation

Explanation

Dilation enlarges or shrinks an object, altering its shape and size.

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

180 degrees

Explanation

The sum of interior angles in a triangle is always 180 degrees.

Which property is not preserved under a rotation transformation?

Orientation

Explanation

Rotation preserves distances and angles but not the orientation of objects.

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

(-3, 4)

Explanation

Reflection over the y-axis negates the x-coordinate.

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

8√2

Explanation

In a 45-45-90 triangle, the hypotenuse is √2 times the length of each leg.

Which matrix represents a reflection over the x-axis?

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

Explanation

The matrix [[1, 0], [0, -1]] reflects points over the x-axis.

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)

Explanation

Dilation multiplies each coordinate by the scale factor.

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

The same figure rotated 180 degrees

Explanation

The composition results in a 180-degree rotation of the original figure.

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?

(2x, 2y)

Explanation

The coordinates of points are multiplied by the scale factor during dilation.

#10

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

k^2πr^2

Explanation

Area scales by the square of the dilation factor.

#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

Explanation

The transformed x-coordinate is calculated using the matrix elements.

#12

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

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

Explanation

The angles determine the arrangement of shapes around a vertex in a tessellation.

Geometric Transformations and Properties Quiz

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

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

Which property is not preserved under a rotation transformation?

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

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

Which matrix represents a reflection over the x-axis?

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?

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

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?

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

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?

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

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