Coordinate Geometry

Link of the Day

Today is Veterans Day, a day set aside to thank those who have risked their lives to serve our country.  As you gather historical, current, and literary examples for your SAT essay, consider including an example involving soldiers.  Think about the courage that it takes to be willing to serve in such a capacity, and the reasons behind the choice to enlist.  Take a look at this article and think about how our lives are different due to the sacrifices of many veterans.

11/11 Coordinate Geometry

Read the following SAT test question and then select the correct answer. 

Use the same process for every math problem.  Read the problem carefully.  Identify the bottom line.  Assess your options, then choose the most efficient method to attack the problem.  Once you have worked the problem, loop back to verify that you have solved for the bottom line.

 math image
In the figure above, which quadrants contain pairs (x, y) that satisfy the condition  x over y = 1?

Bottom line:  Where can you find an x and a y that work for this problem?

Assess your options:  This question concerns coordinate geometry, so you will have to use the facts that you know about graphing to answer the question.  You could pick specific points in each quadrant to see if they work, but simply knowing the properties of the graph should be enough to get you to the answer.

Attack the problem:  In order to divide a number by another number and get one, you need equal numbers.  To satisfy this condition, x and y must be equal to each other.  Ask yourself whether the x and y can be equal to each other in each quadrant.  In quadrant I, all the numbers are positive (+, +), so it is possible for x and y to equal each other and create a positive 1 after division.

Now think about the characteristics of quadrant II.  In quadrant II, all of the x values are negative and all of the y values are positive (-, +), so x and y cannot be equal.  When you divide a negative number by a positive number, you will get a negative number; there is no way to get a positive 1.  Quadrant II does not satisfy this condition.

In quadrant III x and y are both negative (-, -), so they could be equal.  If you divide a negative number by a negative number, the result will be positive.  You can get a positive number 1 in this quadrant.

In quadrant IV, the x values are positive while the y values are negative (+, -).  Once again x and y cannot be equal.  You cannot divide a positive by a negative and get a positive number, so quadrant IV does not satisfy this condition.

Loop Back:  You checked all four quadrants, so look down at your answer choices now.

(A) I only
(B) I and II only
(C) I and III only
(D) II and IV only
(E) I, II, III, and IV

The correct answer is (C).

On, 59% of the responses were correct.

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