b00gigi wrote:

In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?

(1) If the slope of m is y and the slope of n is z, then –yz = 1.

(2) m has a slope of –1, and n passes through the point (–x, –x).

Dear

b00gigi,

I'm happy to help with this.

You may find these blogs helpful:

http://magoosh.com/gmat/2012/gmat-math- ... x-y-plane/http://magoosh.com/gmat/2012/gmat-math- ... lar-lines/In this problem, we know the two lines pass through the origin, (0, 0). That's significant.

Statement #1If the slope of m is y and the slope of n is z, then –yz = 1.

Perpendicular lines in the x-y plan have slopes that are

negative reciprocals. For example,

If one has a slope = 7, the perpendicular line has a slope of –1/7

If one has a slope = 3/5, the perpendicular line has a slope of –5/3

If one has a slope = –4, the perpendicular line has a slope of +1/4

If one has a slope = –8/11, the perpendicular line has a slope of +11/8

Another way to say that is: the product of the slopes of perpendicular lines is -1. Well, if –yz = 1, then yz = –1, and the lines are perpendicular.

This statement, alone and by itself, was enough to answer the prompt question, so it is

sufficient.

Statement #2m has a slope of –1, and n passes through the point (–x, –x).OK, so the slope of line m is –1. Put that on hold.

If n passes through (–x, –x) and (0, 0), then change in y equals change in x, and the slope is +1. Thus, it is perpendicular to line m.

This statement, alone and by itself, was enough to answer the prompt question, so it is

sufficient.

Answer =

(D)Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)