How do you determine the scale factor of dilation?

If a dilation) (or scaling) is given, it is assumed that its center and a factor are given, so we can construct an image of any point.

Step-by-step explanation:

If center of dilation is point  O  and factor is  f ≠ 0 , any given point  A  is transformed by a dilation into point  A '  such that  (a) points  O ,  A  and  A '  are on the same line; (b) if  f > 0 , points  A  and  A '  are on the same side from center  O ; if  f < 0 , point  O  is in between  A  and  A ' ; (c) Lengths of segments  O A '  and  O A  relate to each other at factor  | f| f| , that is  | O A ' | | O A | = | f |

If these two parameters, the center and the factor, are not known, something must be given to determine them.

If a center  O  is given, to determine a factor we need points  A  and its image (the result of scaling)  A ' .

Then, knowing mutual position of points  O ,  A  and  A '  and lengths of segments  O A  and  O A ' , we can determine a factor, its sign based on position of given points and its absolute value as the ratio of the lengths of segments  O A '  and  O A .

If even a center is not given, we need two pairs of points: sources  

A  and  B  and their images  A ' and  B ' .

Then we determine the center as an intersection of lines  A A '  and  B B '  and then follow the procedure above since a center is known now.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

need more information

step-by-step explanation: