Triangle efg is dilated by a scale factor of 1/2
centered at (1, 1) to create triangle e'f'g' which statement is true about the dilation?
the slope of ef is the same as the slope of e'h'
e'g' will overlap eg
gf and gf both pass through the center of dilation
ef = e'f

GF and G'F' both pass through the center of dilation

Step-by-step explanation:

we know that

If two figures are similar, then the corresponding sides are proportional and the corresponding angles are congruent

so

Verify each statement

case A) The slope of EF is the same as the slope of E'H'

The statement is false

Because, after the dilation, the slopes of the corresponding sides are equal

EF and E'F' are not corresponding sides

so

mEF=mE'F'

mFG=mF'G'

mEG=mE'G'

mEH=mE'H'

case B) E'G' will overlap EG

The statement is false

Because the length of the image E'G' is equal to multiply the length of the pre-image EG by the scale factor

The scale factor is 1/2

E'G'=EG(1/2)

therefore

E'G' < EG

case C) GF and G'F' both pass through the center of dilation

The statement is true

Because, the coordinates of point F will be the same than the coordinates of point F' (the center of dilation don't move)

case D) EF=E'F'

The statement is false

Because the length of the image E'F' is equal to multiply the length of the pre-image EF by the scale factor

The scale factor is 1/2

E'F'=EF(1/2)

therefore

E'F' < EF