Answer:
Labelled the given figure triangle as A, B and C.
In triangle ABC;
The coordinates of ABC are:
A = (0, 4)
B = (-2, 10) and
C = (-6, 8)
To find the image of this figure after a dilation with a scale factor of [tex]\frac{1}{2}[/tex] centered at the point O=(2, 2).
The rule of dilation with scale factor [tex]\frac{1}{2}[/tex] centered at the point (2, 2) is given by;
[tex](x, y) \rightarrow (\frac{1}{2}(x-2) +2 , \frac{1}{2}(y-2) +2)[/tex]
or
[tex](x, y) \rightarrow (\frac{1}{2}x+1 , \frac{1}{2}y+1)[/tex]
The coordinate of the image of the figure after dilation are;
[tex]A(0, 4) \rightarrow A'(\frac{1}{2}(0)+1 , \frac{1}{2}(4)+1)[/tex] = A'(1, 3)
[tex]B(-2, 10) \rightarrow B'(\frac{1}{2}(-2)+1 , \frac{1}{2}(10)+1)[/tex] = B'(0, 6)
[tex]C(-6, 8) \rightarrow C'(\frac{1}{2}(-6)+1 , \frac{1}{2}(8)+1)[/tex] = C'(-2, 5)
You can see the graph as shown below in the attachment:
