Question

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?

Answer 1

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

`(x,y)\to (kx,ky)`

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

`(x,y)\to (3.5x,3.5y)`

Using this rule, we get

`(1,4)\to (3.5(1),3.5(4))`

`(1,4)\to (3.5,14)`

Similarly,

`(7,3)\to (3.5(7),3.5(3))`

`(7,3)\to (24.5,10.5)`

`(3,-5)\to (3.5(3),3.5(-5))`

`(3,-5)\to (10.5,-17.5)`

And,

`(8,4)\to (3.5(8),3.5(4))`

`(8,4)\to (28,14)`

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).