Question

dilation ( d_{v, \frac{2}{5}} ) was performed on a rectangle. how does the image relate to the pre - image? choose three correct answers.
the side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image.
the angles of the image are two - fifths the size of the angles of the pre - image.
the base of the image is two - fifths the size of the base of the pre - image.
the center of dilation is at point ( q ).
the image is a reduction because ( 0lt nlt1 ).

Explanation:

• Dilation \(D_{V,\frac{2}{5}}\) means the scale factor \(n = \frac{2}{5}\). For a dilation, if \(0 < n<1\), it is a reduction. The side - lengths of the image are \(n\) times the side - lengths of the pre - image. So the side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image. Also, the base (a type of side) of the image is two - fifths the size of the base of the pre - image. Angles in a dilation are congruent (i.e., the measure of angles does not change). The center of dilation is given as point \(V\) (from the notation \(D_{V,\frac{2}{5}}\)), not \(Q\).

Answer:

• The side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image.
• The base of the image is two - fifths the size of the base of the pre - image.
• The image is a reduction because \(0 < n<1\).