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If the points A (6,1) B(8, 2)c (9,4) and D (P, 3) arevertices of a parallelogram, takenin order Find the value of p C (9,4)D (P,3)A (6, 1)B (8,2) |
Answer» ★Given:-★To find:-
★Solution:-✦Diagonals of a parallelogram bisect each other. Hence,coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD. Using the mid-point formula, ✦(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2] Where,
Midpoint of AC:- →(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2] →(6+9)/2 , (1+4)/2 →15/2 , 5/2 Midpoint of BD:- →(x,y) = [(x₁+x₂)/2, (y₁+y₂)/2] →(8+p)/2 , (2+3)/2 →(8+p)/2 , 5/2 We have the CONDITION: Coordinates of the mid-point of diagonal AC are same as the coordinates of the mid-point of diagonal BD. Therefore, →(8+p)/2 , 5/2 = 15/2 , 5/2 →(8+p)/2 = 15/2 →8+p = 15 →p = 15 - 8 →p = 7 Therefore,the value of p is 7. ______________ |
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