German County is planning to expand its train service. In studying the current service, the county planner looked at which train stations are along or not along various train lines.

The Venn Diagram shows this information for three of the lines.

a. Which train lines that have a stop at Jena?

b. How many stations are along both the Purple Line and the Blue Line?

c. Which stations are along all three lines, (Purple, Orange and Blue Lines)

a. Blue and orange train lines

b. 2

c. Cadiz York

Step-by-step explanation:

Given: Venn diagram

To find:

a. train lines that have a stop at Jena

b. Number of stations along both the Purple Line and the Blue Line

c. stations that are along all three lines

Solution:

A Venn diagram is a pictorial representation of mathematical sets such that as circles are drawn within a rectangle which represents an universal set.

a. Blue and orange train lines have a stop at Jena.

b. Volos Bern and Cadiz York lie in the intersecting part of blue line stations and purple line stations.

So,

Number of stations along both the Purple Line and the Blue Line = 2

c. Cadiz York lie in the intersecting part of blue line stations, purple line stations and orange line stations.

So, Cadiz York lie along all three lines

the correct answer is option c.   3

step-by-step explanation:

points to remember

equation of the line with coordinates (x₁, y₁) and (x₂, y₂) is given by,

slope m = (y₂ - y₁)/(x₂ - x₁)

from the figure we can see a line with two coordinates given

to find the slope of given line

here   (x₁, y₁)   = (-1, -1 ) and (x₂, y₂) = (1, 5)

slope m = (y₂ - y₁)/(x₂ - x₁)

  = (5 - -1)/(1 - -1)

  = (5 + 1)/(1 + 1)

  = 6/2 = 3

therefore the correct answer is option c.   3