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
[tex](x,y)\to (kx,ky)[/tex]
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
[tex](x,y)\to (3.5x,3.5y)[/tex]
Using this rule, we get
[tex](1,4)\to (3.5(1),3.5(4))[/tex]
[tex](1,4)\to (3.5,14)[/tex]
Similarly,
[tex](7,3)\to (3.5(7),3.5(3))[/tex]
[tex](7,3)\to (24.5,10.5)[/tex]
[tex](3,-5)\to (3.5(3),3.5(-5))[/tex]
[tex](3,-5)\to (10.5,-17.5)[/tex]
And,
[tex](8,4)\to (3.5(8),3.5(4))[/tex]
[tex](8,4)\to (28,14)[/tex]
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).
