Coordinate Geometry: Solving a Question for 0P

[Mo]

Another question here .. i attempted it but did not get the correct answer.I will state the question and the steps i took as well.

QUESTION:
"A line is drawn through the point (2,3) making an angle of 45 degrees with the positive direction of the x-axis, and it meets the line x=6 at P.Find the distance of P from the origin 0, and the equation of the line through P perpendicular to 0P"

Steps i took:

1)Since i have to find out the distance of 0P i need to have the Y value of the point P. I assumed the X value is 6 (well, they tell you that anyway)

2)To work out the Y value of P i figured that it needs to be worked out by using the equation of the line (2,3). (ie substitue in an X value to the equation of the line (2,3) to get the Y value of point P)

3)However, to work out the equation of the line (2,3), i also have to know the gradient.I worked this out to be 3/2 (Is this right?)

4)Next i found the equation of the line (2,3) and then i substitued in the X value of P (6) .I found the Y-value to be 12. (Is this right?)

5)Now i work out the length of the line (0,0)(6,12) , and it comes out to be: squareroot of 180

Hmm .. I am sure all of this is not needed .. i bet (hope/wish) someone will come out with a one line asnwer!

Anyway, any help whatsoever is appreciated

Regards,
Mo

 

[Doc Al]

1)Since i have to find out the distance of 0P i need to have the Y value of the point P. I assumed the X value is 6 (well, they tell you that anyway)

OK.

2)To work out the Y value of P i figured that it needs to be worked out by using the equation of the line (2,3). (ie substitue in an X value to the equation of the line (2,3) to get the Y value of point P)

OK.

3)However, to work out the equation of the line (2,3), i also have to know the gradient.I worked this out to be 3/2 (Is this right?)

The slope of the line is 1 (it's at a 45 degree angle), so the equation of the line is y = x + 1. (Perhaps you mistakenly thought that the line goes through the origin? That's how you might have gotten slope = 3/2.)

4)Next i found the equation of the line (2,3) and then i substitued in the X value of P (6) .I found the Y-value to be 12. (Is this right?)

No, because you have the wrong equation for the line.

Using the correct equation, the point P is (6,7). So find the distance to the origin.

To find the equation of the line through P that is perpendicular to the line OP, do this: First find the slope of OP; then find the slope of the perpendicular line. Then, using the point P, find the equation for that line.

 

[Mo]

The slope of the line is 1 (it's at a 45 degree angle), so the equation of the line is y = x + 1. (Perhaps you mistakenly thought that the line goes through the origin? That's how you might have gotten slope = 3/2.)

Yes. Thats where i fell down! .All of the questions i have had so far was involving the line going through the origin. But now i see why they said 45 degrees as well.The answer i now get is correct according to the answer sheet.

Thanks for your help again.

Regards,
Mo