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GRE Quantitative Practice, Complex Multiple-Choice

Question 4

Among the following sets of two xy-coordinate points, which ones define a line on the xy-plane perpendicular to the line defined by the equation y = 4x – 2 ?

Indicate the three correct answer choices.

A.  (2,0) and (–2,1)

B.  (0,–2) and (2,6)

C.  (–2,3) and (–6,4)

D.  (–1,4) and (0,0)

E.  (–3,2) and (3,4)

F.  (0,3) and (4,2)

Explanatory Answer

The standard form for the equation of a line is y = mx + b. The variable m indicates the line's slope, which in this case is 4 (a positive slope). Any line perpendicular to this one must have a slope of –1/4 (the negative reciprocal of 4). To determine the slope of a line defined by the coordinate points supplied in an answer choice, divide the change in y by the corresponding change in x. In other words, determine "rise over run."

The calculations are very simple. For choices (A), (C) and (F) the quotient (slope) is –1/4, and so all three are correct answers. For choice (B) the quotient is 4. For choice (D) the quotient is –4. For choice (E) the quotient is 1/3. Choices (B), (D) and (E) are incorrect.

The correct answer is (A), (C) and (F). You would gain credit for a correct answer only by selecting all three of these choices but no others.