{"id":417,"date":"2020-06-10T07:22:02","date_gmt":"2020-06-10T07:22:02","guid":{"rendered":"https:\/\/blog.prepbytes.com\/?p=417"},"modified":"2022-03-30T23:00:43","modified_gmt":"2022-03-30T23:00:43","slug":"quadrilateral","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/quadrilateral\/","title":{"rendered":"Quadrilateral"},"content":{"rendered":"

\"\"<\/p>\n

CONCEPTS USED:<\/h3>\n
\n

Basic Mathematics, Co-ordinate Geometry<\/p>\n<\/blockquote>\n

DIFFICULTY LEVEL:<\/h3>\n
\n

Easy<\/p>\n<\/blockquote>\n

PROBLEM STATEMENT(<\/code>SIMPLIFIED)<\/code>:<\/h3>\n
\n

Given 4 coordinate points, check if the given quadrilateral formed from given coordinates forms a Square or not, print Yes<\/code> or No<\/code> accordingly.<\/p>\n<\/blockquote>\n

<\/strong><\/u><\/a><\/p>\n

EXAMPLE:<\/h4>\n
Input: A(20, 10), B(10, 20), C(20, 20), D(10, 10)\n\nOutput: Yes\n\nExplanation: Diagonals are of same length and bisect at same coordinates.\n\nd1 = (20 - 10)*(20 - 10) + (10 - 20)*(10 - 20) = 200\nd1 = (20 - 10)*(20 - 10) + (20 - 10)*(20 - 10) = 200\n\nmid1 = ( (20 + 10)\/2 , (10 + 20)\/2 ) = (15, 15)\nmid2 = ( (20 + 10)\/2 , (20 + 10)\/2 ) = (15, 15)<\/code><\/pre>\n
OBSERVATION:<\/h3>\n
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Proving that the given Quadrilateral is a Square<\/code> solves our problem as it has all its sides equal.<\/p>\n
\n
Properties of Square<\/code>: <\/p>\n
    \n
  1. \n
    Both diagonals are of the same length.  <\/p>\n<\/li>\n
  2. \n
    Both diagonals bisect at the same coordinates.<\/p>\n<\/li>\n<\/ol>\n<\/blockquote>\n<\/blockquote>\n
    SOLVING APPROACH:<\/h3>\n
    \n
      \n
    1. \n
      If the length of both diagonals are equal and they bisect each other at the same coordinates, then return Yes<\/code> else No<\/code>.<\/p>\n<\/li>\n
    2. \n
      Find the length of both the diagonals using the given formula :<\/p>\n
      √(X{2} \u2212 X<\/em>{1})2<\/sup> + `(Y{2} \u2212 Y<\/em>{1})2<\/sup><\/span><\/p>\n<\/li>\n
    3. \n
      Find the mid point of both the diagonals using the following mid-point theorem :<\/p>\n
      X<\/code> = (<\/code>X_{1} + X_{2}<\/code>)<\/code> \/<\/code> 2<\/p>\n
      Y<\/code> = (<\/code>Y_{1} + Y_{2}<\/code>)<\/code> \/<\/code> 2<\/p>\n<\/li>\n<\/ol>\n<\/blockquote>\n
      SOLUTIONS:<\/h3>\n
      \t\t\t\t\t\t