By definition:
- Reflection is a transformation in which an object is flipped.
- Dilation is a transformation in which the shape of the object does not change, but its size does.
- The Pre-Image is the object before the transformation and the Image is the object transformated.
- The rule for a reflection over the x-axis is the following:
[tex](x,y)\rightarrow\mleft(x,-y\mright)[/tex]- The rule of a dilation centered at the origin, with the scale factor
[tex]\frac{1}{2}[/tex]is the following:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]Knowing the above, you can conclude that rule for the transformation given in the exercise, is:
[tex](x,y)\rightarrow(\frac{1}{2}x,-\frac{1}{2}y)[/tex]Knowing that the Pre-Image is:
[tex]\mleft(-2,10\mright)[/tex]You get that the Image of that point is:
[tex]\begin{gathered} \mleft(-2,10\mright)\rightarrow(\frac{1}{2}(-2),-\frac{1}{2}(10)) \\ \\ (-2,10)\rightarrow(-1,-5) \end{gathered}[/tex]The answer is:
[tex](-1,-5)[/tex]