# 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* = 4*x* – 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*.