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SAT Math: Geometry

Coordinate Geometry

If a line passes through the points  (4, 6) and (16, 24), which of the following points does the line also pass through?

A.   (4, 24)

B.   (6, 8)

C.   (6, 14)

D.   (8, 12)

E.   (16, 22)

 

Knowsys Method

Read the question carefully.  As you read, try to envision the two points that you have been given on a graph.

Identify the bottom line.  You must find a point that lies on the same line as the two points you have been given.

 Assess your options.  There are many ways that you could solve this problem.  You could draw a graph, but that will take a while because you have no graph paper.  You could try to create an equation for the line and find the slope of the line, but there is still a faster way.  There are many points that lie along this line, so eventually you will have to look at the answers to see which is an answer choice.  Start by looking at the answer choices.  Often, when you see "which of the following," the answer will be D or E because most students look at the first answer choice first.  Start with the last answer choice.

Attack the problem.  If you quickly look over the answer choices, you will notice that all of them would lie between the points that are given.  What would be the easiest point to find between the two points?  The midpoint!  It will be halfway between the points (4, 6) and (16, 24).  You could use the midpoint formula, but you can use logic to find the midpoint.  What is halfway between 4 and 16 (your x values)?  The number 8.  What is halfway between 6 and 24 (your y values)?  The number 12.  Your new point is (8, 12).  Even if this is not the answer, it should help you be able to evaluate the other answer choices.  Look down at the answer choices, starting with E.

E.  This answer is not correct, and you will know that if you envisioned the line on the coordinate graph as you read the points.  You started out with a point with small numbers and then both numbers got bigger.  That means that you have a diagonal line going up.  The only way that your point could have the same number as one of the other points in the line is if the line were horizontal or vertical.  (16, 22) and (16, 24) would create a vertical line that would never pass through (4, 6).  Eliminate this choice.

D.  This is the midpoint between the two points!  

Loop back.  You only needed to find one point that works, so you are finished!

 

The correct answer is (D). 

This is a medium level question.

 

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