Universal scale. suppose we wanted to make a scale model of the local group or galaxies in which the milky way galaxy was the size of a doughnut (-10 cm in diameter).
a) how far from the milky way would the andromeda galaxy be on this scale?
b) how far would the sun be from alpha centauri on this scale? can you name an object that has a size comparable to this distance?
c) how far would it be from the milky way galaxy to the most distant galaxies in the observable universe on this scale?

a) x₁ = 236.5 cm , b)   x₂ = 4.1 10⁻⁴ cm , cells, c)  x3 = 1.23 10⁶ cm

Explanation:

It is requested to build a scale model of several star systems, to begin we must look for the distances to the two desired systems and use a direct proportions rule, where the rule is that the dialect of the milky way (105700 y) is equivalent to 10 cm

a) Distance to the Andromeda galaxy, the closest to the milky way

      d = 2.5 106 y

Where the ano-light is the most used unit of measure that equals the distance traveled by the light in one year (y = 9,461 1012 km)

Since the distances are so great we can consider the bodies as punctual,

            x₁ = 2.5 106 y (10 cm / 105700 y)

            x₁ = 236.5 cm

b) The distance from the sun to alpha centuri

          d₂ = 4.37 y

          x₂ = 4.37 y (10 cm / 105700 y)

          x₂ = 4.1 10⁻⁴ cm

This size is of the order of the diameter of most cells

c) the most distant galaxy known is called EGS-ZS8-1 is at a distance of 13000 10⁶ y

           x3 = 13000 10⁶ (10 cm / 105700)

           x3 = 1.23 10⁶ cm

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

insects!

explanation: