Answer:
Given: A scale factor of [tex]\frac{1}{2}[/tex].
Let centre of dilation at origin.
As we can see that the vertices of the triangle at (0,0), (0,2) and (4,0) forms a right triangle.
Dilation states that the transformation that produces an image that is the same shape as the original, but of a different size.
The rule for Dilation is [tex](x,y) \rightarrow (kx ,ky)[/tex] where k is the scale factor i.e, [tex]k = \frac{1}{2}[/tex]
or we can write the rule as :[tex](x,y) \rightarrow (\frac{1}{2}x ,\frac{1}{2}y)[/tex]
Multiply the each coordinates of the triangle by [tex]\frac{1}{2}[/tex], to find the coordinates for the dilation of the triangle.
(0,0) [tex]\rightarrow[/tex] [tex](\frac{1}{2}\cdot 0 ,\frac{1}{2}\cdot 0 ) = (0,0)[/tex]
(0,2) [tex]\rightarrow (\frac{1}{2}\cdot 0, \frac{1}{2}\cdot 2)[/tex] = (0,1)
and (4,0) [tex]\rightarrow (\frac{1}{2}\cdot 4 , \frac{1}{2} \cdot 0)[/tex] = (2,0)
Therefore, the coordinate after the dilation are (0,0) , (0,1) and (2,0).
We plot a graph for both the triangle in coordinate plane:
