Darselle wrote:
So when I did this I guessed that it would form a square like that too and chose the correct answer. But can anyone explain to me intuitively why we can connect these four dots and consider that the enclosed area ? Thanks
Hello,
Darselle. My guess is that if you had already solved the question in the manner outlined above, then you already understand the intuitive reasoning behind the solution. Since the equation places an absolute value around
each unknown and sets their sum equal to 5, and since absolute value can be thought of as a distance from 0, you are effectively testing extremes by setting one unknown to its highest and lowest values while holding the other at 0. That is, once you set
x at -5, for instance, you can only set
y to 0. You can derive all four "extreme" points in this manner. Connecting them with segments graphically shows that for any
valid x or
y value tested within the constraints of the problem, the sum of the distance from 0 does not exceed 5. You can test easier points for reference, such as (-1, 4) or (3, -2), but you cannot break from the figure. In fact, if you tested enough points from the infinite number of possible
x and
y values--decimals would just give you more and more points to test--you would create the figure itself. An earlier poster had suggested values of -3 and 8 for the unknowns, but such a combination would violate the absolute value principles at work: -3 is 3 away from 0, which is fine, but 8 is 8 away from 0, and there is no negative absolute value that could pull the sum back to 5. So in short, I would suggest that you attempt to break free of the "box." As long as you observe that the total distance of the sum cannot exceed 5, you can test all you want, and you will only ever create a more and more refined box. It is not an issue of "Why can we?" but more an issue of "How can we not?"
- Andrew