Question

select the correct answer.

which statement corrects the error, or errors, in this definition?

in a dilation, each point in the preimage and its corresponding point in the image are at equal distances from a given line. also, the line segment joining two such points is perpendicular to the given line.

• a dilation is when an object moves in a circular arc around a point.
• a dilation moves points a specified distance along a line parallel to a specified line.
• a dilation proportionally stretches or compresses an object based on a given scale factor.
• the definition is correct.

Explanation:

Analyze the given definition

The provided statement defines a transformation: "In a dilation, each point in the preimage and its corresponding point in the image are at equal distances from a given line. Also, the line segment joining two such points is perpendicular to the given line."

Using the Geometric Transformations knowledge point, we identify that this is actually the definition of a reflection across a line, not a dilation.

Evaluate the options

Using the Dilations in the Coordinate Plane knowledge point:

• Option 1 describes a rotation ("moves in a circular arc around a point").
• Option 2 describes a translation or glide reflection.
• Option 3 correctly defines a dilation: "A dilation proportionally stretches or compresses an object based on a given scale factor."
• Option 4 is incorrect because the original definition describes a reflection, not a dilation.

Select the correct statement

The third option correctly identifies the true definition of a dilation, correcting the error in the prompt's definition.

Answer:

• (A) A dilation is when an object moves in a circular arc around a point.
• (B) A dilation moves points a specified distance along a line parallel to a specified line.
• (C) A dilation proportionally stretches or compresses an object based on a given scale factor. (Correct answer)
• (D) The definition is correct.