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

Solution:

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

$k=\frac{1}{2}$

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

$\begin{gathered} S^{\prime}(kx,ky)\Rightarrow S^{\prime}(\frac{1}{2}\times8,\frac{1}{2}\times-4) \\ \Rightarrow S^{\prime}(4,-2) \end{gathered}$

Hence,

The final answer is = ( 4, -2)