Question

What are the coordinates of Point S after a dilation with the canter at the origin and a scale factor of 1/2

Answer 1

Concept:

With the center being at the origin, the dilation formula for the shape below will be given below as

`\begin{gathered} S(x,y)\Rightarrow S^(\prime)(kx,ky) \\ \text{Where,} \\ k=\text{scale factor} \end{gathered}`

From the graph below,

The coordinates of point S is given as

`S(8,-4)`

The scale factor is given as

`k=(1)/(2)`

By applying the dilation formula above, we will have the coordinate of point S after dilation be

`\begin{gathered} S^(\prime)(kx,ky)\Rightarrow S^(\prime)((1)/(2)*8,(1)/(2)*-4) \\ \Rightarrow S^(\prime)(4,-2) \end{gathered}`

Hence,

The final answer is = ( 4, -2)