A quadrilateral has vertices at (1.4). (7,3), (3, -5), and (8,4). The
quadrilateral is dilated by a scale
factor of 3.5 with the origin as its
center. What are the coordinates of
the vertices of the image of the
quadrilateral?

Given:

A quadrilateral has vertices at (1,4), (7,3), (3, -5), and (8,4).

The quadrilateral is dilated by a scale factor of 3.5 with the origin as its center.

To find:

The coordinates of the vertices of the image of the quadrilateral.

Solution:

If a figure is dilated by a scale factor k with origin as it center, then

It is given that the quadrilateral is dilated by a scale factor of 3.5 with the origin as its center. So, the rule of dilation is

Using this rule, we get

Similarly,

And,

Therefore, the coordinates of the vertices of the image of the quadrilateral are (3.5,14), (24.5,10.5), (10.5,-17.5), (28,14).