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Coordinate Geometry Core 1

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1. Hi guys,

I'm doing some maths revision and can't seem to get the right answer for this question.

The question says Find the equation of the straight line, p, which is the perpendicular bisector of the points (1,2) and (5,4). The line p meets the x axis at A and meets the y axis at B. Calculate the area of the triangle OAB.

So far this is what I've got:
The gradient of the line joining the two points (I'll call them C and D) is 1/2 and c is 3/2 making the equation of the straight line between C and D y=1/2x+3/2
The midpoint of C and D is (3,3) and the perpendicular bisector must have the gradient of -2 meaning c=9. This means that the equation of the perpendicular bisector is y=-2x+9 which the book answer agrees with.
Because p is then perpendicular to this line the gradient must be 1/2 so so far our line p has the equation of y=1/2x+c but I can't seem to work out what c is. I know that A is (?,0) and B is (0,?) meaning when x is 0 (at B) y=c
I know that the area of the triangle is given by 1/2bh but the fact that I can't find c is preventing me from finding the area.

Thanks in advance for any help,
Blake
2. (Original post by Blake Jones)
Hi guys,

I'm doing some maths revision and can't seem to get the right answer for this question.

The question says Find the equation of the straight line, p, which is the perpendicular bisector of the points (1,2) and (5,4). The line p meets the x axis at A and meets the y axis at B. Calculate the area of the triangle OAB.

So far this is what I've got:
The gradient of the line joining the two points (I'll call them C and D) is 1/2 and c is 3/2 making the equation of the straight line between C and D y=1/2x+3/2
The midpoint of C and D is (3,3) and the perpendicular bisector must have the gradient of -2 meaning c=9. This means that the equation of the perpendicular bisector is y=-2x+9 which the book answer agrees with.
Good.

Because p is then perpendicular to this line
No. This line (y=-2x+9) is p. This is the perpendicular bisector.
3. (Original post by ghostwalker)
Good.

No. This line (y=-2x+9) is p. This is the perpendicular bisector.
Oh! Thank you!!! Need to learn to read the question more carefully! Thanks!

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