A straight water pipeline passes through two points with map references (3,2) and (7,-1) respectively.The shortest spur pipe from the pipeline to farm P is PN. Find:

a) the coordinates of N.
b) the length of the pipeline spur from N to P given that the grid reference scale is 1 unit=0.5km.

Question

A straight water pipeline passes through two points with map references (3,2) and (7,-1) respectively.The shortest spur pipe from the pipeline to farm P is PN. Find:

a) the coordinates of N.
b) the length of the pipeline spur from N to P given that the grid reference scale is 1 unit=0.5km.

mathmate · Answer

It looks to me that the coordinates of P should be given.
Can you please check the question?

anonymous · Answer

P's coordinates are 9,7

mathmate · Answer

Ah!
First you will need to find the equation of the major pipe which passes through (3,2) and (7,-1).
Have you already done that?

anonymous · Answer

wouldn't there be two equations? y+x=6 and -y+x=2? then I would solve them simultaneously

anonymous · Answer

i'm not sure if they're right but my coordinates for N are 4,2

mathmate · Answer

We would first find the equation A for the pipe that passes through the two given points.  From that equation, we would determine the slope a1, and hence deduce the slope of PN, a2, which is perpendicular to the major pipe.
Then we will construct an equation B with slope a2 that passes through P.
The intersection of A and B will give the point N.
Subsequently the length PN can be calculated since P and N are then both known.

Note:
x+y=6 does not pass through both given points, nor does -y+x=2.

anonymous · Answer

thank you for your help... i'll try to get right

mathmate · Answer

Hint: N lies between the two given points, and the coordinates of N are not integers.