Line g is dilated by a scale factor of one half from the origin to create line g'. where are points e' and f' located after dilation, and how are lines g and g' related?

Third option.

Step-by-step explanation:

In this case you know that the line was dilated from the origin to create the line  . The scale factor used was:

So you can conclude that the lenght of the segment E'F'  will be shorter that the lenght of the segment EF. Since the lenghts change by the same proportion, the image and the pre-image will be parallel.

Notice in the graph that the coordinates points E and F located on the line  , are:

Therefore, in order to find the coordinates of the points E' anf F', you must multiply the coordinates of the points E and F by the scale factor. Then:

E'→  

F'→

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3