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Coordinate Geometry and line equation

Here is a question which I need help on:

Find the equation of the straight line (in the form ax+by+c=0 where a,b and c are integers) which is the perpendicular bisector the line through (4,9) and (-2,1).

Here are the main parts of my long working out:

I found the midpoint of the line through (4,9) and (-2,1) to be (1,5)

(1,5)=(x1, y1)

The gradient of the line through (4,9) and (-2,1) is 86\frac{8}{6}
Therefore the gradient of the perpendicular bisector must be 68-\frac{6}{8}

y5=68(x1)y-5=-\frac{6}{8}(x-1)

y5=68x+68y-5=-\frac{6}{8}x+\frac{6}{8}

8(y5)=6x+68(y-5)=-6x+6

Therefore my answer is the following:
6x+8y46=06x+8y-46=0

This is incorrect, because the correct answer is 3x+4y-23=0:confused:
What have I done wrong???:confused::confused:

Thanks a lot for any help provided.
Reply 1
Original post by krisshP
Here is a question which I need help on:

Find the equation of the straight line (in the form ax+by+c=0 where a,b and c are integers) which is the perpendicular bisector the line through (4,9) and (-2,1).

Here are the main parts of my long working out:

I found the midpoint of the line through (4,9) and (-2,1) to be (1,5)

(1,5)=(x1, y1)

The gradient of the line through (4,9) and (-2,1) is 86\frac{8}{6}
Therefore the gradient of the perpendicular bisector must be 68-\frac{6}{8}

y5=68(x1)y-5=-\frac{6}{8}(x-1)

y5=68x+68y-5=-\frac{6}{8}x+\frac{6}{8}

8(y5)=6x+68(y-5)=-6x+6

Therefore my answer is the following:
6x+8y46=06x+8y-46=0

This is incorrect, because the correct answer is 3x+4y-23=0:confused:
What have I done wrong???:confused::confused:

Thanks a lot for any help provided.


You haven't done anything wrong, I don't think. They've just divided the equation by two or simplified the perpendicular bisector gradient 68-\frac{6}{8} to 34-\frac{3}{4} :smile:

Your answer is still fine, though :smile:
(edited 11 years ago)
Reply 2
Original post by usycool1
You haven't done anything wrong, I don't think. They've just divided the equation by two :smile:


So if my answer to this type of question is simply a multiple of the correct answer, does this mean I will be correct always in this case?
Reply 3
Original post by krisshP
So if my answer to this type of question is simply a multiple of the correct answer, does this mean I will be correct always in this case?


It should be OK as usually in a mark scheme it says "oe" next to the answer which means "or equivalent"
(edited 11 years ago)
Reply 4
Original post by usycool1
It should be OK as usually in a mark scheme they write "oe" next to the answer which means "or equivalent"


It's just that I haven't done any past papers for A-level Maths - the only practice is from a revision book.

Thanks a LOT for your help :smile::smile::smile::smile:
Reply 5
Original post by krisshP
It's just that I haven't done any past papers for A-level Maths - the only practice is from a revision book.

Thanks a LOT for your help :smile::smile::smile::smile:


I see :smile:

No problem :biggrin:

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