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# Coordinate Geometry and line equation

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1. 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
Therefore the gradient of the perpendicular bisector must be

Therefore my answer is the following:

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

Thanks a lot for any help provided.
2. (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
Therefore the gradient of the perpendicular bisector must be

Therefore my answer is the following:

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

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 to

3. (Original post by usycool1)
You haven't done anything wrong, I don't think. They've just divided the equation by two
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?
4. (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"
5. (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
6. (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
I see

No problem

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