Prime number, array_multiplication and Cartesian planes

Array multiplication

a = [2,4,5,6]

#product increment
times= 1

#starting value
start = 0
result = []
#loop through the array to get the product
  a.each{|i| times = times * i}
  
 #loop through the array and divide the product by the elements of the array
  a.each{|i| result<<times/i}
  
  #output the result
  puts result

Cartesian Planes

#This program takes in two arrays containing
#the x and y coordinates, the breadth i.e x axis and
#the length i.e y-axis

a=[2,1,3,3]
b=[3,3,4,3]
def array_intersection(a,b)
    r1x1 = a[0]
    r1y1 = a[1]
    r1x2 = a[0]
    r1y2= a[1] + a[2]
    r1x3 = a[0] + a[3]
    r1y3 = a[1] + a[2]
    r1x4 = a[0] + a[3]
    r1y4 = a[1]

    puts "coordinates of First Rectangle"
    puts "x1: #{r1x1}  y1: #{r1y1}"
    puts "x2: #{r1x2}  y2: #{r1y2}"
    puts "x3: #{r1x3}  y3: #{r1y3}"
    puts "x4: #{r1x4}  y4: #{r1y4}"

    r2x1 = b[0]
    r2y1= b[1]
    r2x2 = b[0]
    r2y2 = b[1] + b[2]
    r2x3 = b[0] + b[3]
    r2y3= b[1] + b[2]
    r2x4 = b[0] + b[3]
    r2y4 = b[1]

    puts "coordinates of Second Rectangle"
    puts "x1: #{r2x1}  y1: #{r2y1}"
    puts "x2: #{r2x2}  y2: #{r2y2}"
    puts "x3: #{r2x3}  y3: #{r2y3}"
    puts "x4: #{r2x4}  y4: #{r2y4}"

    x_points = [r1x1,r1x4,r2x1,r2x4].sort!
    y_points = [r1y1,r1y3,r2y1,r2y2].sort!

    x= x_points - x_points.minmax
    y= y_points - y_points.minmax
    puts ''
    puts "Intersection Points"
    puts "x1: #{x[0]} , y1: #{y[0]}"
    puts "x2: #{x[0]} , y2: #{y[1]}"
    puts "x3: #{x[1]} , y3: #{y[0]}"
    puts "x4: #{x[1]} , y4: #{y[1]}"
  end

  array_intersection(a,b)

Prime Number using Square roots

#this method calculates the mid-poit of the 
#two arguments

def mid(x,y)
  midpoint = (x + y)/2.0
end

#this method uses the square-root method to get
#ths square-root of a number and loops through 
#from 2 to the square-root to verify if it is a 
#prime number or not

def prime(value,n)
  check = true
  #get the square-root
  num = sqrt(value,n)

  #roundup the number to an integer
  n = num.round
  start = 2
  #loop through and test if it is prime or not
  while start <=n
    if value % start == 0
      check = false
    end
    start =start + 1
  end
  check
end

#this function gives thw square-root of a number
#using the trial method
def sqrt(n,d)
  lower_range = 0
  higher_range = n
  div = mid(higher_range,lower_range)
    until (div * div) - n <=  d and (div * div) -n >= 0 do
    higher_range = div if (div * div) - n > d
    lower_range = div if (div * div) - n < 0
    div =mid(lower_range,higher_range)
    
  end
  div
end

puts prime(7,0.0000001)