First, identify the coordinates of the points A, B and C:
[tex]\begin{gathered} A=(-2,4) \\ B=(4,2) \\ C=(-2,0) \end{gathered}[/tex]
The rule for the transformation of a dilation by a scale factor k is:
[tex](x,y)\rightarrow(kx,ky)[/tex]
Apply the dilation by a factor of 1/2 to the points A, B and C to find their images A', B', C':
[tex]\begin{gathered} A(-2,4)\rightarrow A^{\prime}(\frac{1}{2}\times-2,\frac{1}{2}\times4)=A^{\prime}(-1,2) \\ \\ B(4,2)\rightarrow B^{\prime}(\frac{1}{2}\times4,\frac{1}{2}\times2)=B^{\prime}(2,1) \\ \\ C(-2,0)\rightarrow C^{\prime}(\frac{1}{2}\times-2,\frac{1}{2}\times0)=C^{\prime}(-1,0) \end{gathered}[/tex]
Plot the images A'(-1,2), B'(2,1) and C'(-1,0) to graph the dilation image of the triangle ABC with a scale factor of 1/2:
