A parallelogram has three of its vertices (1, 2), (3, 8) and (4, 1). The sum of ordinates of all possible coordinates of the fourth vertex is:
Answers
(6 , 7) , (0 , 9) & (2 , - 5) are all possible fourth vertex if A parallelogram has three of its vertices (1, 2), (3, 8) and (4, 1)
Step-by-step explanation:
A parallelogram has three of its vertices (1, 2), (3, 8) and (4, 1)
Three possibilities
Sides (1 , 2) - ( 3 , 8) & (1, 2) - ( 4, 1) Diagonal ( 3 , 8)( 4, 1)
Sides ( 4, 1) ( 3 , 8) & (1, 2) - ( 4, 1) Diagonal (1 , 2) - ( 3 , 8)
Sides ( 4, 1) ( 3 , 8) & (1 , 2) - ( 3 , 8) Diagonal (1, 2) - ( 4, 1)
Case 1 :
Sides (1 , 2) - ( 3 , 8) & (1, 2) - ( 4, 1) Diagonal ( 3 , 8)( 4, 1)
Fourth vertex (x , y)
(y - 8)/(x - 3) = (1-2)/(4-1)
=> (y - 8)/(x - 3) = -1/3
=> 3y - 24 = -x + 3
=> x + 3y = 27
(y - 1)/(x - 4) = (8 - 2)/(3 - 1)
=> (y - 1)/(x - 4) = 6/2
=> (y - 1)/(x - 4) = 3
=> y - 1 = 3x - 12
=> 3x - y = 11
10x = 60
=> x = 6
y = 7
(6 , 7) is fourth vertex
Case 2 :
Sides ( 4, 1) ( 3 , 8) & (1, 2) - ( 4, 1) Diagonal (1 , 2) - ( 3 , 8)
Fourth vertex (x , y)
(y - 8)/(x - 3) = (1-2)/(4-1)
=> (y - 8)/(x - 3) = -1/3
=> 3y - 24 = -x + 3
=> x + 3y = 27
(y - 2)/(x - 1) = (8 - 1)/(3 - 4)
=> (y - 2)/(x - 1) = -7
=> y - 2 = -7x + 7
=> 7x + y = 9
x = 0 & y = 9
(0 , 9) is fourth vertex
Case 3 :
Sides ( 4, 1) ( 3 , 8) & (1 , 2) - ( 3 , 8) Diagonal (1, 2) - ( 4, 1)
(y - 2)/(x - 1) = (8 - 1)/(3 - 4)
=> (y - 2)/(x - 1) = -7
=> y - 2 = -7x + 7
=> 7x + y = 9
(y - 1)/(x - 4) = (8 - 2)/(3 - 1)
=> (y - 1)/(x - 4) = 6/2
=> (y - 1)/(x - 4) = 3
=> y - 1 = 3x - 12
=> 3x - y = 11
x = 2 y = -5
(2 , - 5) is fourth vertex
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Answer:
Step-by-step explanation:just used the concept of mid point Of diagonals
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