In the xy plane point P (m,n) and point Q (n,m) what is the

Question

In the xy plane point P (m,n) and point Q (n,m) what is the distance between P and Q

(1) m - n = 2
(2) m + n = 5

Bunuel · Accepted Answer

The formula to calculate the distance between two points  (x_1,y_1)  and  (x_2,y_2)  is  d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} .

So we are asked to calculate:  d=\sqrt{(m-n)^2+(m-n)^2}=\sqrt{2(m-n)^2}=\sqrt{2}*|m-n| .

(1)  m-n=2 . Sufficient.

(2)  m+n=5 . Not sufficient.

Answer: A.

gurpreetsingh · Answer

Distance between two points  (x_1,y_1)  and  (x_2,y_2)  is  \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

put the values you will get  \sqrt{(m - n)^2 + (n - m)^2}

=  \sqrt{2(m - n)^2}

Hence A is sufficient.

rxs0005 · Answer

Thanks Gentlemen for the algebraic approach i was using the graphical approach and was confused

adishail · Answer

A .

You can not rely on the graphical solution. I mean you can plot it, but then eventually you will have to play with the equation for distance between two points.

shrouded1 · Answer

Actually you can solve this graphically. What you need to note is that points (m,n) and (n,m) are mirror reflections across the x=y (45 degree) line on the coordinate plane.

And the final piece in the puzzle is, if you draw a horizontal and a vertical line from (m,n) & the point (n,m) to intersect x=y, both lines will intersect at the points (m,m) and (n,n). This square you form has side (m-n) & its diagnol is the straight line joining (m,n) and (n,m)

So distance = Sqrt(2) * (m-n)

Hence all you need is m-n

The solution seems a bit involved, but if you draw it out it'll be pretty straight forward.

adishail · Answer

Actually, it is the same thing as plotting two points and then writing the equation of distance between two points. As far as being a faster way, the fact that the pyth theorem uses a difference is enough to get the soultion.

shrouded1 · Answer

Ultimately it has to be the same thing, same problem same solution ... just saying that you can solve the question by plotting a graph and without knowing the distance formula

Alternate solution if you may

josemnz83 · Answer

I'm not understanding how A is sufficient to answer the question. All A says is that m-n=2. What about n-m? How are m-n and n-m the same?

mau5 · Answer

(m-n) and (n-m) are not the same thing, however, (m-n)^2 and (n-m)^2 are the same thing. Take (m-n) = 2, thus (n-m) = -2. However, (m-n)^2 = (n-m)^2 = 4.

aakrity · Answer

I solved this question by drawing a rough diagram.

Option A > m-n = 2 which means OP = 2, OQ =2

Since OPQ is a right triangle, we can easily calculate the distance PQ.  Sufficient

Option B > m+n = 2, clearly insufficient to come to any solution

Correct answer A.

Jaikuz · Answer

In the xy-plane, point P has coordinates (m; n) and point Q has coordinates (n;m). What is the distance between P and Q?

(1) m - n = 2 
(2) m + n = 5

Hello,

I will be more than happy if you can help me with the explanation please as I do not see much difference between (1) and (2).

Bunuel · Answer

Merging topics. Please refer to the discussion above.

OptimusPrepJanielle · Answer

There is a lot of difference between 1 and 2.

The sign makes all the difference. Distance between two points (x_1, y_1) and (x_2, y_2) = ^(1/2) In the given question, Distance = ^(1/2) Since this formula uses a - sign, we can solve this by using the statement 1, but not statement 2. Does this help?

Senthil7 · Answer

The distance would be Square root of (m-n)^2 + (n-m)^2 therefore m-n = 5 can be substituted in this equation to obtain the actual distance. The second one gives value of m+n that cannot be utilized without further info in this equation hence  A .

shashankism · Answer

The points in the xy plane are P(m,n) and Q(n,m)

Distance between points P & Q = sqrt{(m-n)^2+(n-m)^2)} 
=  sqrt{2} |m-n|

Question : Distance between P & Q

Statement 1: we know value of m-n = 2
So, Distance = 2  sqrt{2} 
 Sufficient

Statement 2 : m+n = 5, so we can't find the value of m-n from this.
So, Distance can't be found out uniquely.
 Insufficient

Answer A

Take care when using statement 2, otherwise you can do a silly mistake and mark option D instead of A.

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