Question 1019527: If the points A(1,-2),B(2,3),C(a,2),D(-4,-3) form a parallelogram,find the value of a hence find the height of the parallelogram
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Using your coords
Work out the gradient of AB and DC
AB = y2 - y1/x2 - x1 = 3 - (-2)/2 - 1 = 5/1
DC = y2 - y1/x2 - x1 = 2 - (-3)/a - (-4) = 2 + 3/a + 4
AC has the same gradient as DC (parallelogram opposite sides)
DC = 5/ a + 4 = 5/1
Cross multiply
5 = 5(a + 4)
5 = 5a + 20
5a = -15
a = -3
C (-3,2)
Height of parallelogram
Using DC
D(-4,-3) C(-3,2)
Distance formula:
√(x2 - x1)^2 + y^2 - y1)^2
√ (-3 - (-4))^2 + (2 - (-3)
√(1)^2 + (5)^2
√ 26
= 5.1 units (1 decimal place)
Hope this helps :-)
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