SOLUTION: 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 respectivel

Question 1118633: 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 squared. Find the value(s) of k
Found 2 solutions by t0hierry, Boreal:
Answer by t0hierry(194) (Show Source): You can put this solution on YOUR website!
x/4 + y/8 = k
x=0 y = 8k B(0,8k)
y=0 x = 4k A(4k.0)
The area is half the product of OA and OB since these are perpendicular.
So 1/2 32 k^2 = 144
or 16 k^2 = 144
4 k = 12
k = 3
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
multiply everything by 8
2x+y=8k
y=-2x+8k
when y=0 (x-axis), 8k=2x and k=(1/4)x or x=4k
when x=0 (y-axis) y=8k
(4k, 0) and (0, 8k)
When the third point is (0, 0), the base is 4k and the height is 8k
The area is (1/2)32k^2=144 u^2
32k^2=288
k^2=9 and k=3 ANSWER
y=-2x+24

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