Geometry: Coordinate Geometry
Read the following SAT test question and then select the correct answer.
Always be sure to read the question carefully and make a note of the bottom line. Then assess your options and choose the most efficient method to attack the problem. When you have an answer, loop back to verify that it matches the bottom line.
In the xy-plane, line l passes through the points (a, 0) and (0, 2a), where a > 1. What is the slope of line l?
Bottom Line: slope of l = ?
Assess Your Options: You could select a number larger than 1, plug it in for the variable a, and then work the problem. However, if you peek down at the answer choices, notice that some have a variable still in the problem. It will take you longer to plug in a number than to work the problem using the variables.
Attack the Problem: Your bottom line is a slope, so use the formula for the slope of a line. The formula for slope of a line is:
To find the change in y coordinates, subtract the first y-value from the second y-value. Do the same with the x values:
The variable will cancel when you simplify the problem. Your answer is -2.
Loop Back: You found the slope of the line, so you are ready to look down at your answer choices.
On sat.collegeboard.org, 42% of the responses were correct.
For more help with SAT math, visit www.myknowsys.com!
Link of the Day
On this day in 1968, James Earl Ray, an escaped American convict, was arrested and charged with the assassination of Dr. Martin Luther King. Ray was in the process of trying to escape Rhodesia when he was apprehended. He was eventually convicted and sentenced to 99 years in prison. You can read more about James Earl Ray here.
6/8 Calculating the slope of a Line
Read the following SAT test question and then click on a button to select your answer.
The first step here is to identify the bottom line. In this case we are looking for the slope of a line that is perpendicular to the line that passes through the points (0,0) and (2,5). The first step to answering this problem is to calculate the slope of the line that passes through the points given. Remember that the slope of a line is equal to the rise over the run so you have
It is essential that you don't forget to answer the bottom line for this question. Although this is a fairly easy question, it is very easy to make a sloppy mistake and miss some easy points. We are looking for the slope of a line that is perpendicular to the line that passes through the points given. The slope of a perpendicular line is always the negative reciprocal of the slope of the line it is perpendicular to. So we take the original slope we calculated, negate it, and flip it.
Now we simply look at the answers and choose the answer that matches our prediction.
As you can see, answer B matches our prediction exactly. Note that if we had failed to answer the bottom line and only calculated the slope of the line that went through the points, we would have picked answer (D). Even though this was a fairly easy problem, more than 50% of the responses were incorrect!
On sat.collegeboard.com 49% of the responses were correct.
For more help with math, visit www.myknowsys.com!