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Question 1118698: Consider the line x/4 + y/8 = k where k is a positive number.
a) In terms of k, write down the coordinates of A and B, the points where the line meets the x and y axes respectively.
b) The area of triangle AOB, where O is the origin, is 144 units^2. Find the value(s) of k.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider the line x/4 + y/8 = k where k is a positive number.
a) In terms of k, write down the coordinates of A and B, the points where the line meets the x and y axes respectively.
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Meets x axis means y = 0::
x/4 + 0/8 = k
x = 4k
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Meets y axis means x = 0::
0/4 + y/8 = k
y = 8k
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b) The area of triangle AOB, where O is the origin, is 144 units^2. Find the value(s) of k.
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Plot the points:: A(4k,0) and B(0,8k) and O(0,0)
Notice the triangle AOB.
base = 4k
altitude = 8k
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Equation:
(1/2)(4k)(8k) = 144 u^2
16k^2 = 144 u^2
k^2 = 9 u^2
k = 3 units
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Cheers,
Stan H.
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