GMAT Math : DSQ: Calculating whether lines are perpendicular
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Example Questions
Example Question #1 : Lines
Data Sufficiency Question
Is Line A perpendicular to the following line?
Statement 1: The slope of Line A is 3.
Statement 2: Line A passes through the point (2,3).
Each statement alone is sufficient.
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.
Statement 1 alone is sufficient, but Statement 2 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but Statement 1 alone is not sufficient to answer the question.
Statement 1 alone is sufficient, but Statement 2 alone is not sufficient to answer the question.
To determine if two lines are perpendicular, only the slope needs to be considered. The slopes of perpendicular lines are the negative reciprocals of each other. Knowing a single point on the line is not sufficient, as an infinite number of lines can pass through and individual point.
Example Question #1 : Geometry
Refer to the above figure. True or false:
Statement 1: 
Statement 2: Line 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 alone establishes nothing about the angle 
Assume both statements are true. Then 
Example Question #2 : Lines
Statement 1:
Refer to the above figure. Are the lines perpendicular?
Statement 1:
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. The measure of one of the angles formed is
Assume Statement 2 alone.
By substituting 
The marked angles are a linear pair and thus their angle measures add up to 180 degrees; therefore, we can set up an equation:
Example Question #2 : Geometry
Refer to the above figure.
True or false:
Statement 1:
Statement 2:
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 alone establishes by definition that 
By Statement 2 alone, since alternating interior angles are congruent, 
Assume both statements are true. By Statement 2, 
Example Question #3 : Lines
Refer to the above figure. True or false:
Statement 1:
Statement 2: Line 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. Then, as a consequence of congruence, 
Assume Statement 2 alone. Then 
Example Question #5 : Geometry
The equations of two lines are:
Are these lines perpendicular?
Statement 1:
Statement 2:
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.
The lines of the two equations must have slopes that are the opposites of each others reciprocals.
Write each equation in slope-intercept form:
As can be seen, knowing the value of 
The answer is that Statement 1 alone is sufficient to answer the question, but Statement 2 alone is not sufficient to answer the question.
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