Question

The coordinates of trapezoid EFGH are E(4, 8), F(1, 2), G(6, 1), and H(8, 8). The image of EFGH under dilation is E'F'G'H'. If the coordinates of vertex H' are (4, 4), what are the coordinates of vertex E'?
(1,2)
(2,4)
(2,2)
(0,4)

Answer 1

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)