Line segment AB has endpoints A(1, 4) and B(2, 8). A dilation, centered at the origin, is applied to AB¯¯¯¯¯. The image has endpoints A′(18, 12) and B′(14, 1). What is the scale factor of the dilation?

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

8

step-by-step explanation:

i think the answer is b