Question

te figure abcd by a scale factor of \\(\frac{1}{2}\\) with the center of dilation at the origin.\
i the coordinates of the vertices\
the dilated image.\
ure abcd figure abcd\
a(4,4) a(2,2)\
b(6,2) b(3,1)\
c(6,6)?\
d(4,8) c(1,3)\
c(3,3)\
c(6,3)\
c(12,12)

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) with center at the origin and scale factor \(k\), the new coordinates are \((kx, ky)\). Here, \(k = \frac{1}{2}\) and the point \(C\) is \((6,6)\).

Step2: Apply dilation formula

For point \(C(6,6)\), multiply each coordinate by \(\frac{1}{2}\). So, \(x'=\frac{1}{2}\times6 = 3\) and \(y'=\frac{1}{2}\times6 = 3\). Thus, the coordinates of \(C'\) are \((3,3)\).

Answer:

\(C'(3,3)\)