The image of EFGH under dilation is E'F'G'H'. If the coordnates of Vertex H' are (4,4), the coordinates of vertex E' are (2,4)
Second option (2,4)
Solution:
The point H has coordinates (8,8)
H=(8,8)=(xh,yh)→xh=8, yh=8
If the coordinates of vertex H' are (4,4)
H'=(4,4)=(xh',yh')→xh'=4, yh'=4
The factor of dilation "f" is:
f=xh'/xh=yh'/yh
f=4/8=4/8
f=4/8
Simplifying the fraction, dividing the numerator and denominator by 4:
f=(4/4)/(8/4)
f=1/2
Then we must multiply the original coordinates of EFGH by f=1/2 to obtain the new coordinates E'F'G'H'. Then, the coordinates of E' are:
E=(4,8)=(xe,ye)→xe=4, ye=8
xe'=f xe→xe'=(1/2) 4→xe'=4/2→xe'=2
ye'=f ye→ye'=(1/2) 8→ye'=8/2→ye'=4
E'=(xe',ye')→E'=(2,4)
