Hi phanikpk,
Many graphing questions are made easier if you physically graph them on the pad. In this question, you have the vertices of a straight-forward rectangle. The question then states that the rectangle will be cut into 2 equal areas. There are many different ways to cut a rectangle into 2 pieces with equal areas, BUT the question goes on to state that the line/cut must pass through the co-ordinate (2,2).
After graphing that point and taking a look at the answer choices, you should be able to see that the correct answer IS one of the EASIEST ways to cut the area of the rectangle in half - cutting from left to right, right across the middle. This line has a slope of 0
Final Answer: A
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What is the slope?
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Here is what it would look like on your scratch paper.
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To partition the rectangle into equal areas, the line must pass through the CENTER of the rectangle.The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4
To determine the x-coordinate of the center, take the average of the x-coordinates that form the base:
(0+7)/2 = 3.5.
To determine the y-coordinate of the center, take the average of the y-coordinates that form the left side:
(0+4)/2 = 2.
Thus, the center of the rectangle = (3.5, 2).
Since the line must pass through (2, 2) and (3.5, 2), we get the following slope:
(2 - 2)/(3.5 - 2) = 0.
The correct answer is A.
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Brent@GMATPrepNow
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This questions illustrates the importance of ALWAYS checking the answer choices BEFORE getting bogged down with time-consuming calculations. For more on this important strategy, you can watch our free video: https://www.gmatprepnow.com/module/gener ... es?id=1111The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4
We should first sketch the rectangle...
From here, we must draw a line through (2,2) that cuts the rectangle into 2 regions that have equal areas.
Without resorting to complicated equations, we might see a quick way to make such a cut. However, if we don't see this quick way, we should check out the answer choices.
Answer choice A suggests that a line of slope zero might work.
If we try it, we get...
...perfect! It clearly cuts the rectangle into 2 equal pieces.
DONE!
Answer: A
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
