# A Level Maths: Coordinate Geometry

Watch
Announcements

Could someone help me with this?

A point P lies on the line with equation y = 4 - 3x. The point P is a distance of square root 34 from the origin. Find the two possible positions of point P.

I’ve been trying to work it out for so long and I just can’t get my head around it.

A point P lies on the line with equation y = 4 - 3x. The point P is a distance of square root 34 from the origin. Find the two possible positions of point P.

I’ve been trying to work it out for so long and I just can’t get my head around it.

1

reply

Report

#2

(Original post by

Could someone help me with this?

A point P lies on the line with equation y = 4 - 3x. The point P is a distance of square root 34 from the origin. Find the two possible positions of point P.

I’ve been trying to work it out for so long and I just can’t get my head around it.

**fortuneandero**)Could someone help me with this?

A point P lies on the line with equation y = 4 - 3x. The point P is a distance of square root 34 from the origin. Find the two possible positions of point P.

I’ve been trying to work it out for so long and I just can’t get my head around it.

0

reply

(Original post by

Draw the line on a graph, there will be two points root 34 away from the origin on that line.

**Howie_2114**)Draw the line on a graph, there will be two points root 34 away from the origin on that line.

0

reply

Report

#4

Let p have coordinates (x,y). We want to find the possible values of x and y.

First set up an equation using the distance formula.

Can you work from there?

First set up an equation using the distance formula.

Can you work from there?

0

reply

But I don’t understand where I would go from there to find two possible positions of point P

0

reply

Report

#8

(Original post by

Would it be root 34 = root (x^2 + y^2) ?

**fortuneandero**)Would it be root 34 = root (x^2 + y^2) ?

As P(x.y) lies on the line y = 4 - 3x, the coordinates satisfy that equation.

So now, because they both have y as the subject, you can equate your distance equation with the equation of the straight line.

0

reply

Report

#9

(Original post by

Good so far, Now square both sides to get rid of the square roots and rearrange to make y the subject.

As P(x.y) lies on the line y = 4 - 3x, the coordinates satisfy that equation.

So now, because they both have y as the subject, you can equate your distance equation with the equation of the straight line.

**razzor**)Good so far, Now square both sides to get rid of the square roots and rearrange to make y the subject.

As P(x.y) lies on the line y = 4 - 3x, the coordinates satisfy that equation.

So now, because they both have y as the subject, you can equate your distance equation with the equation of the straight line.

0

reply

Report

#10

(Original post by

Yes but that’s gonna take longer than just substituting values and getting 34

**LowIQ**)Yes but that’s gonna take longer than just substituting values and getting 34

0

reply

**razzor**)

Good so far, Now square both sides to get rid of the square roots and rearrange to make y the subject.

As P(x.y) lies on the line y = 4 - 3x, the coordinates satisfy that equation.

So now, because they both have y as the subject, you can equate your distance equation with the equation of the straight line.

0

reply

Report

#12

(Original post by

Trial and error will take much longer as there is more than one possible set of coordinates for P.

**razzor**)Trial and error will take much longer as there is more than one possible set of coordinates for P.

0

reply

Report

#13

(Original post by

I’ve done this so far

**fortuneandero**)I’ve done this so far

0

reply

(Original post by

Yes but forget the root as it’s the same on both sides

**LowIQ**)Yes but forget the root as it’s the same on both sides

0

reply

Report

#18

(Original post by

Oh I see, so I simply expand the y substitution and collect the like terms?

**fortuneandero**)Oh I see, so I simply expand the y substitution and collect the like terms?

0

reply

(Original post by

Yes and it will form a quadratic

**LowIQ**)Yes and it will form a quadratic

0

reply

Report

#20

(Original post by

So then I would just factorise the quadratic and solve for x?

**fortuneandero**)So then I would just factorise the quadratic and solve for x?

0

reply

X

### Quick Reply

Back

to top

to top