Centre of Love!
If L O V E is a quadrilateral with coordinates L = ( 2 , 5 ) , O = ( 6 , 2 ) , V = ( 2 , − 1 ) and E = ( − 2 , 2 ) . Find the meeting point of the diagonals of the quadrilateral. If the meeting point can be written as ( a , b ) , then give your answer as a + b .
Type your answer as 999 if L O V E doesn't form a quadrilateral.
The answer is 4.
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1 solution
I have one more logical solution. Just note that the x − c o o r d i n a t e of L and V is 2 , so, the equation of the line L V must be x = 2 . So, any point on the line L V must have the x − c o o r d i n a t e as 2 . Again, note that the y − c o o r d i n a t e of O and E is 2 , so, the equation of the line O E must be y = 2 . So, any point on the line O E must have the y − c o o r d i n a t e as 2 . Now, the meeting point of the diagonals lies on both the lines L V and O E . So, the above two statements imply that its x − c o o r d i n a t e and y − c o o r d i n a t e both should be 2 . So, the required coordinates are ( 2 , 2 )
Note that LOVE forms a rhombus. Then, using the property that its diagonals bisect each other, simply find the coordinates of the meeting point of the diagonals with the section formula. The coordinates you will get are ( 2 , 2 ) . So, the answer is simply 2 + 2 = 4