Given:
The graph of a rectangle.
The given rectangle is dilated from the origin by a scale factor of 3.
To find:
The vertices of the image of the rectangle after the dilation.
Solution:
From the given graph it is clear that the vertices of the rectangle are A(0,2), B(0,4), C(3,4) and D(3,2).
If a figure is dilated from the origin by a scale factor of 3, then
[tex](x,y)\to (3x,3y)[/tex]
Using this rule, the vertices of the image are:
[tex]A(0,2)\to A'(3(0),3(2))[/tex]
[tex]A(0,2)\to A'(0,6)[/tex]
Similarly,
[tex]B(0,4)\to B'(3(0),3(4))[/tex]
[tex]B(0,4)\to B'(0,12)[/tex]
And,
[tex]C(3,4)\to C'(3(3),3(4))[/tex]
[tex]C(3,4)\to C'(9,12)[/tex]
And,
[tex]D(3,2)\to D'(3(3),3(2))[/tex]
[tex]D(3,2)\to D'(9,6)[/tex]
The vertices of the image after dilation are (0,6), (0,12), (9,12), (9,6).
Therefore, the correct options are B and F.
