Manhattan GMAT Challenge Problem

jrbrown2 · Posted: Tue Jul 10, 2007 9:20 am Post subject: Manhattan GMAT Challenge Problem

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7

(B) 2x + y = –px

(C) x + 2y = px + 7

(D) y – 7 = x ÷ (p – 2)

(E) 2x + y = 7 – px

To start I figured out the slope of line L
Slope = (q-3)/(p-2) = (2-3)/(p-2) = -1/(p-2)
If line M is perpendicular to the line L then M's slope is the negative inverse of line L's slope.

So Slope of line M = (p-2)

The equation of a line is y = mx+b where m is the slope and b is the y intercept. I rewrote all of the answer choices in this form and selected the answer that had the correct slope of (p-2), which is the negative inverse of line L's slope.

(A) 2x + y = px + 7 Therefore Y = (p-2)x +7

(B) 2x + y = –px Therefore Y = (-p-2)x

(C) x + 2y = px + 7 Therefore Y = (p-1)x/2 + 7/2

(D) y – 7 = x ÷ (p – 2) Therefore Y = x/(p-2) + 7

(E) 2x + y = 7 – px Therefore Y = (-p-2)x +7

Choice A is the only choice that has (p-2) as its slope so A is the answer

gabriel · Posted: Wed Jul 11, 2007 6:54 am Post subject:

.. yup ..me too getting A as the answer