What is meant by “explain your work” in Math 120R?
Roughly speaking, this means that you should present your solutions so that
other competent students in the class can easily understand what you are
doing. In this context, keep in mind that this is not a freshman high
school algebra class, where more detailed explanations would be required
that in Math 120R at UA.
Also, in my use of the word “explain”, I do not mean that you have to explain in words what you are doing if it is obvious from your algebra what you are doing. An explanation can be symbolic rather that verbal.
Examples:
Long solution (freshman high school):6x = -3A competent high school student should understand this; no further VERBAL explanation is needed (for your Math 120R-10 instructor).
x = -3/6
x = -1/2
Short solution (for Math 120R):x = -1/2.A competent Math 120R student should easily be able to obtain this answer without further explanation, and no further explanation is needed (for your Math 120R-10 instructor).
Solution. [Just plot it; a competent Math 120R student should easily be able to obtain this answer without further explanation.]
Solution. ... [Don't just write down the answer; show your work, using the formula for midpoint.]
Solution. [You can do this using the midpoint formula again, but this one can also be done “in your head”, and if you do it this way, some words of explanation would be needed, e.g.: ]
Since 2 is halfway between the given x-coordinates, 1 and 3, and since 4 is halfway between the given y-coordinates, 2 and 6, the point halfway between (1, 2) and (3, 6) is the point (2, 4).
[There are many other ways of describing this, but don't just write down the answer (2, 4) without any explanation or work shown.]
Check. It is ALWAYS a good idea to check your work, to see if your answer satisfies the conditions set down in the problem. This is especially important in a case like this, where we have used a somewhat unorthodox method of solving the problem. Our solution is supposed to be a midpoint, so the distance from our solution to the given points should be the same for both points, and it should be half the distance between the given points. (Be sure you understand why this should be true.)
Distance between given points, (1, 2) and (3, 6):
√[(3-1)2 + (6-2)2] = √[4 + 16] = √20 = 2√5.
Distance between first given point, (1, 2), and solution, (2, 4):
√[(2-1)2 + (4-2)2] = √[1 + 4] = √5.
Distance between solution, (2, 4), and second given point, (3, 6):
√[(3-2)2 + (6-4)2] = √[1 + 4] = √5.
So, as it should be, the distance (√5) from our solution to the given points is the same for both points, and it is half the distance (2√5) between the given points.
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