Exploring Geometric Transformations

What is a geometric transformation?

• A geometric transformation is a process of coloring geometric shapes.

• A geometric transformation is a function that modifies the position, size, shape, or orientation of a geometric figure.

• A geometric transformation is a type of geometric figure.

• A geometric transformation is a method for measuring angles.

How do you find the image of a point after a transformation?

• Reflect the point across the origin without applying rules.

• Add a random value to the original coordinates.

• Apply the transformation rules to the original point's coordinates.

• Use the distance formula to calculate the image.

Define translation in the context of geometric transformations.

• Translation is a reflection of a shape across a line.

• Translation is a rotation of a shape around a fixed point.

• Translation is a geometric transformation that moves a shape or object a constant distance in a specified direction.

• Translation refers to resizing a shape to a different scale.

How does a reflection transformation differ from a rotation?

• A reflection rotates a shape around a point, while a rotation creates a mirror image.

• A reflection moves a shape in a straight line, while a rotation flips it over.

• A reflection creates a mirror image, while a rotation turns a shape around a point.

• A reflection changes the size of a shape, while a rotation keeps the size the same.

What is the effect of a dilation on a geometric figure?

• A dilation only affects the angles of a geometric figure.

• A dilation flips a geometric figure over a line.

• A dilation changes the size of a geometric figure while preserving its shape.

• A dilation rotates a geometric figure without changing its size.

Explain the concept of symmetry in geometric transformations.

• Symmetry refers to the color patterns of a shape.

• Symmetry in geometric transformations is the property of a shape remaining unchanged under transformations like reflection, rotation, or translation.

• Symmetry is the process of changing the size of a shape.

• Symmetry only applies to shapes with equal sides.

What are the coordinates of a point after a 90-degree rotation counterclockwise around the origin?

• (y, -x)

• (x, -y)

• (-x, -y)

• (-y, x)

Describe the process of performing a translation on a triangle.

• Reflect the triangle over a line.

• Scale the triangle by a factor.

• To translate a triangle, add the translation vector to each vertex's coordinates.

• Rotate the triangle around a vertex.

How can you determine if two figures are congruent after transformations?

• Two figures are congruent if they can be overlapped without any gaps or overlaps.

• Two figures are congruent if they have the same area but different shapes.

• Two figures are congruent if one can be transformed into the other using translations, rotations, or reflections.

• Two figures are congruent if they have the same color.

What is the matrix representation of a reflection over the x-axis?

• [[0, -1], [-1, 0]]

• [[0, 1], [1, 0]]

• [[1, 0], [0, 1]]

• [[1, 0], [0, -1]]