Question

taking guided notes is an excellent way to stay focused during lessons. they can also be a helpful resource for you to review later. read the sentences below, filling in the blanks with items from this list. each item will be used once. dilation circle translation shape similar radius diameter center scale factor a is the set of all points equidistant from a center. a circle is the set of all points equidistant from a. the distance from the center of a circle to any point on the circle is the. the longest chord in a circle is the. a transformation that enlarges or reduces a figure while preserving its shape is a. the ratio used in a dilation is called the. the transformation used to align the centers of two circles is a. the uniform scaling of all points in a dilation ensures the remains unchanged. all circles are classified as because dilations preserve proportionality.

Explanation:

• A circle is the set of all points equidistant from a center: By the definition of a circle, it is a geometric figure where every point on its boundary is at the same distance (radius) from a fixed point called the center.
• A circle is the set of all points equidistant from a center: This is a restatement of the circle's definition.
• The distance from the center of a circle to any point on the circle is the radius: This is the basic property of a circle's radius.
• The longest chord in a circle is the diameter: A chord is a line segment connecting two points on a circle. The diameter passes through the center, so its length (\(d = 2r\)) is the longest possible chord length.
• A transformation that enlarges or reduces a figure while preserving its shape is a dilation: Dilation is a geometric transformation that changes the size of a figure but not its shape.
• The ratio used in a dilation is called the scale factor: The scale factor \(k\) determines how much a figure is enlarged (\(k>1\)) or reduced (\(0 < k<1\)).
• The transformation used to align the centers of two circles is a translation: Translation is a transformation that slides a figure without rotating or resizing it. Moving one circle to align its center with another is a translation.
• The uniform scaling of all points in a dilation ensures the shape remains unchanged: Dilation preserves the shape of the figure (e.g., a circle remains a circle after dilation).
• All circles are classified as similar because dilations preserve proportionality: Similar figures have the same shape (proportional corresponding parts). Since any circle can be obtained from another by dilation (which preserves proportionality as the ratio of radii is the scale factor), all circles are similar.

Answer:

A. circle
A circle is the set of all points equidistant from a center. center
The distance from the center of a circle to any point on the circle is the radius. radius
The longest chord in a circle is the diameter. diameter
A transformation that enlarges or reduces a figure while preserving its shape is a dilation. dilation
The ratio used in a dilation is called the scale factor. scale factor
The transformation used to align the centers of two circles is a translation. translation
The uniform scaling of all points in a dilation ensures the shape remains unchanged. shape
All circles are classified as similar because dilations preserve proportionality. similar