Line A is drawn on a rectangular coordinate plane. If the coordinate

Question

Line A is drawn on a rectangular coordinate plane. If the coordinate pairs (3, 2) and (-1, -2) lie on line A, which of the following coordinate pairs does NOT lie on a line that is perpendicular to line A?

A. (5, 8) and (4, 9)
B. (3, -1) and (4, -2)
C. (-1, 6) and (-4, 9)
D. (2, 5) and (-3, 2)
E. (7, 1) and (6, 2)

Ashishmathew01081987 · Accepted Answer

The slope intercept form is given by : Y = MX + C
M = Slope
C = Y - intercept

Slope = Rise / Run 
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
M=1

Perpendicular lines have -ve reciprocal slopes i.e. The line perpendicular to the above line will have a slope of -1 and will be of the form 
Y = -X + C

Testing all options that will "NOT" give a slope of -1

a) (5, 8) and (4, 9)
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
 M= -1

b) (3, -1) and (4, -2) 
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
 M= -1

c) (-1, 6) and (-4, 9)
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
 M= -1

d) (2, 5) and (-3, 2) 
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
 M= 3/5

e) (7, 1) and (6, 2)
M = (Y1 - Y2) / (X1 - X2) 
M =   /   
 M= -1

Answer is D

laraterra · Answer

Hi,

Please, how can I solve this question without drawing the plane? I got it right but I had to draw all lines until I found the one that were not perpendicular. It took me almost 8 minutes.

Tks!!

adiagr · Answer

With the given set I can find slope of the line:

\frac{-2-2}{-1-3}  m=  \frac{-4}{-4}  = 1

A line that is perpendicular to above line will have a slope of -1 (Perpendicular line has a slope of (-1/m), where m is slope of original line)

Let us check options

\frac{9-8}{4-5}  = -1 --> This line is perpendicular on given line.
 \frac{-2+1}{4-3}  = -1 --> This line is perpendicular on given line.
 \frac{9-6}{-4+1}  =  \frac{3}{-3}  =-1 --> This line is perpendicular on given line.
 \frac{2-5}{-3-2}  =  \frac{-3}{-5}  = 3/5 -->  This line is NOT perpendicular on given line.

Option D is the answer.

Mehadihasanshawon · Answer

My strategy:
As the question demands to find out the coordinates that not lie on the perpendicular of question mentioned line, which's slope is positive, I have tried to find out the positive slope from the given coordinates using the normal slope formula. 
Another strategy that helps to find out the positive slope is left to right direction and opposite for the negative.

Following the above, I found positive slope at option D.

Posted from my mobile device

TargetMBA007 · Answer

KarishmaB  - Trying to see if there is a more efficient approac to this, that doesnt require calculating slopes for each answer choice. 
Here's my thought proces, but I wonder if its sound? I am looking for a slope of -1 in the choices, as any slope with -1 would not be the answer to the question. Calculating each slope would be time-consuming, but I can see that in each choice, the diff between x coordinates and y coordinates is exactly the same, except in D, where x coordinates differ by 5 and y coordinates by 3, so this must be my answer.

I am guessing, if the correct answer had a slope of 1, then this approach would not hold, but it works for this question?

Line A is drawn on a rectangular coordinate plane. If the coordinate

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GMAT Problem Solving (PS) Questions

Line A is drawn on a rectangular coordinate plane. If the coordinate

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