To solve the problem of finding the coordinates of the point [tex]\( V' \)[/tex] obtained after dilating the point [tex]\( V(2,4) \)[/tex] by a scale factor of 4, follow these steps:
1. Identify the original coordinates:
The original coordinates of the point [tex]\( V \)[/tex] are given as [tex]\( V(2, 4) \)[/tex].
2. Understand the scale factor:
The scale factor of the dilation is given as 4. This means that each coordinate of the original point will be multiplied by 4.
3. Apply the scale factor to each coordinate:
Multiply the x-coordinate and the y-coordinate of the point [tex]\( V \)[/tex] by the scale factor.
[tex]\[
x' = 2 \times 4 = 8
\][/tex]
[tex]\[
y' = 4 \times 4 = 16
\][/tex]
4. Form the new coordinates:
The coordinates of the dilated point [tex]\( V' \)[/tex] are [tex]\( (8, 16) \)[/tex].
Therefore, the coordinates of the point [tex]\( V' \)[/tex] after dilation by a scale factor of 4 are [tex]\( \boxed{(8,16)} \)[/tex].
