Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f'. where are points a' and b' located after dilation, and how are lines f and f' related?

the locations of a' and b' are a' (0, 2) and b' (0, 0); lines f and f' intersect at point a.
the locations of a' and b' are a' (0, 1) and b' (1, 0); lines f and f' are parallel.
the locations of a' and b' are a' (0, 0) and b' (2, 0); lines f and f' intersect at point b.
the locations of a' and b' are a' (0, 2) and b' (2, 0); lines f and f' are the same line.

The locations of A' and B' are A' (0, 1) and B' (1, 0); lines f and f' are parallel.

Step-by-step explanation:

Dilate A and B by one half.

Dilate point A:

(0,2)   0 × 0.5 = 0     2 × 0.5 = 1

A' = (0,1)

Dilate point B:

(2,0)   2 × 0.5 = 1     0 × 0.5 = 0

B' = (1,0)

If you draw a line connecting A' and B' it would be line f'.

This line would be parallel to line f. This is because they do not intersect and they have the same slope.

the correct answer is the second option

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: