Given: A scale factor of 1/2 and center N of a figure is given.
Required: To dilate the given figure using the given scale factor and center.
Explanation: Dilation is a transformation, used to change the size of the given figure. If the value of dilation>1 then the new figure enlarges. If dilation<1 then the given figure contracts while a dilation=1 means that the new figure is of the same size.
Now here the center is given to be N. And the scaling factor is 1/2.
The coordinates of center N are (3,2). Point M is 2 units left and 4 units down from point N. Hence for dilation of a factor of 1/2, point M' will be 1 unit to the left and 2 units down from point N -
[tex]\begin{gathered} M^{\prime}=(3-1,2-2) \\ M^{\prime}=(2,0) \end{gathered}[/tex]
Similarly, point O is 2 units to the right and 6 units down from point N. Hence for dilation of a factor of 1/2, point O' will be 1 unit to the right and 3 units down from point N.
[tex]\begin{gathered} O^{\prime}=(3+1,2-3) \\ =(4,-1) \end{gathered}[/tex]
Final Answer: M'=(2,0)
O'=(4,-1)
