Coordinate Geometry

Link of the Day

Isn't it fascinating that no matter how long people study people, there is still more to learn?  Take a look at this current event article that endeavors to explain why women talk more than men.  Pick out the broad topics in this article.  How could you use the facts from this article to support a position on the following SAT essay prompts?

1. Do we need other people in order to understand ourselves?
2. Should heroes be defined as people who say what they think when we ourselves lack the courage to say it?
3. Are people best defined by what they do?

Geometry: Coordinate Geometry

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

Always read the question carefully and identify the bottom line.  Assess your options for reaching the bottom line and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that the answer matches the bottom line.

What is the equation of the line parallel to the x-axis and four units above the x-axis?

Bottom Line: equation of a line

Assess your Options:  You could look down at the answer choices, but if you look down without thinking first you will often confuse yourself.  Instead, use the information that you are given to write an equation.

Attack the Problem:  You know that you are dealing with an x-axis, which means you must use a normal xy-graph with a vertical y-axis and a horizontal x-axis.  Draw this on your paper.  Next, imagine 4 ticks on the y-axis and put a little dot four units above the x-axis.  Draw a horizontal line that is parallel to the x-axis.  Does that line ever leave y = 4?  No!  That is the equation of the line.

Note:  If you write x = 4, you create a vertical line.  Think about it this way: the x values change from negative infinity to positive infinity.  If you choose a single x value, the line along this value cannot be parallel to the x-axis because it is limited to a single value.

Loop Back:  You needed an equation of a line, and not necessarily one that mentioned x at all.  You found one.  Look down at your answer choices.

(A) x = -4

(B) x = 4

(C) y = -4

(D) y = 0

(E) y = 4

The correct answer is (E).

On sat.collegeboard.org, 67% of the responses were correct.

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