Question

What is the image point (-2,10) after reflecting over the x axis and dilating by 1/2

Answer 1

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:

`(x,y)\rightarrow\mleft(x,-y\mright)`

- The rule of a dilation centered at the origin, with the scale factor

`(1)/(2)`

is the following:

`(x,y)\rightarrow((1)/(2)x,(1)/(2)y)`

Knowing the above, you can conclude that rule for the transformation given in the exercise, is:

`(x,y)\rightarrow((1)/(2)x,-(1)/(2)y)`

Knowing that the Pre-Image is:

`\mleft(-2,10\mright)`

You get that the Image of that point is:

`\begin{gathered} \mleft(-2,10\mright)\rightarrow((1)/(2)(-2),-(1)/(2)(10)) \\ \\ (-2,10)\rightarrow(-1,-5) \end{gathered}`

The answer is:

`(-1,-5)`