25. If the points A(5, 3), B(8,5), C(x, y) and
D(7, 2) are consecutive vertices of a
parallelogram, then (x, y) =
Answers
check the attachment ................
Given : points A(5, 3), B(8,5), C(x, y) and D(7, 2) are consecutive vertices of a parallelogram
To find : (x, y)
Solution:
A(5, 3), B(8,5)
Slope of AB = (5 - 3)/(8 - 5 ) = 2/3
C(x, y) D(7, 2)
Slope of CD = ( y - 2)/(x - 7)
opposites sides of parallelogram area parallel
parallel lines have equal slope
Slope of AB = Slope of CD
( y - 2)/(x - 7) = 2/3
=> 3y - 6 = 2x - 14
=> 2x = 3y + 8
A(5, 3) D(7, 2)
Slope of AD = (2 - 3)/(7 - 5) = -1/2
B(8,5) C(x, y)
Slope of BC = (y - 5)/(x - 8)
(y - 5)/(x - 8) = -1/2
=> 2y - 10 = - x + 8
=> x + 2y = 18
=> 2x = 36 - 4y
3y + 8 = 36 - 4y
=> 7y = 28
=> y = 4
x + 2y = 18 => x + 2(4) = 18 => x + 8 = 18
=> x = 10
(x, y) = = ( 10 , 4)
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