In the xy-coordinate system, what is the slope of the line

Question

In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

KillerSquirrel · Answer

line equation = Y = a*X + b A = slope P (1,11) Q (7,7) (1+7)/2, (11+7)/2 equidistant = (4,9) origin = (0,0) slope = (Y2-Y1)/(X2-X1) = 9/4 check: 9 = a*4+b 0 = a*0+b b = 0 a = slope = 9/4 :-D

iamba · Answer

You are correct, but think about this:

If the line passing thru origin is equidistant from P and Q, then it must be a parpendicular bisector of the line that connects P and Q. Hence its slope must be negative reciprocal of PQ.

Now, PQ has a slope of -4/6 or -2/3. So slope of the bisector should be 3/2.

Can you point out where am I going wrong?

thanks

KillerSquirrel · Answer

The line doesn't has to be parpendicular bisector of the line that connects P and Q - see the attached drawing for visualisation, hence your assumption is wrong (sorry).

iamba · Answer

Thanks, but let me bug you little more..

The line is equidistant means that every point on the line is equidistant from P and Q, right? 
If yes, then do you think the origin is equidistant from both P and Q?

Balvinder · Answer

iamba, ur point is valid 

also there is one more case if a line passing thru origin and is paralle to line passing thru the given 2 points then also the perpendicular distance is equal.

In that case the slope will be same as that of given line that means -2/3.

where as question is asking of a line where all point are equidistance.

i think we need more detail in this question..

vshaunak@gmail.com · Answer

The case suggested by Balvinder is valid. Question is asking for the parellel line passing through the origin. 

Another case is - where the line is passing through the origin and perpendicular bisector of PQ. This case is NOT possible for the given set of points as the line, joining the origin and mid point of PQ, is not perpendicular to PQ.

iamba · Answer

Anyway, OA is 9/4.

Balvinder, the parallel line passing thru origin does not satisfy the condition because all points on this line will not be equidistant from P and Q.

Balvinder · Answer

iamba, 

even for the line which is passing thru the mid point of given points P and Q and from origin i,e the first case,

 all points on this line are not equidistant from P and Q.


Only mid point is equidistant from the point P and Q.

iamba · Answer

Balvinder,

I am not saying that the first graph provided by KillerSquirrel is accurate. Both explainations have the same limitation that all points are not equidistant from P and Q.

But still the OA is 9/4 as obtained by using the formula to find the midpoints of a St. line.

On G- day I would chose 9/4

In the xy-coordinate system, what is the slope of the line

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards