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

GMAT assassins aren't born, they're made,
Rich

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

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=1111

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

Cheers,
Brent