Question 21 - Final question on higher paper

thomas49th

I cant think of a way to "show that y=....". Do I compare to x values?

Thx

neutrino

Given coordinates of two points on the plane, how would you find the distance between them? Write down mathematically what the statement says and solve for y.

symbolipoint

Just use the Distance Formula. This is the typical way of helping new students of Intermediate Algebra to understand parabolas. Your textbook probably also shows an example like the question which you asked.

HallsofIvy

What IS the distance from a point (x,y) to (0, 2)?
What IS the distance from a point (x,y) to the x-axis?

Since the problem tells you that those two distances are the same write down those two formulas and set them equal.

thomas49th

(x,y) - (x,0) = (x,y) -(0,2)

is that right?

Hootenanny

Does this ring any bells;

[tex]d = \sqrt{\left(x_1-x_0\right)^2+\left(y_1-y_0\right)^2}[/tex]

HallsofIvy

I don't even know what that means!

I know how to subtract numbers.
I even know how to subtract vectors.

How do you subtract points?

thomas49th

LHS

x - x = 0
y - 0 = y

RHS
x - 0 = x
y - 2 = y - 2

SO

y = x + y - 2

x = 2

that right?

neutrino

Nooo!

Take a look at Hootenanny's post.

thomas49th

ive never ever seen that formula in my life, and I think it is beyond GCSE level (that exams you do in UK when your 15 or 16). Is that formula the simplest way?

neutrino

I thought most people would have seen that formula at least a couple of years before they turn 16!

Given any two points (x0,y0) and (x1,y1), the distance between them is given by that formula. It's just the Pythagorean theorem done on the Cartesian plane. In three dimensions, there would also be the (z1-z0)² within the square root.

cristo

Is it not just Pythagoras' Theorem in a different guise?

thomas49th

how would cristo go about solving it then?

Rhythmer

It is. You're right.

thomas49th

is it just me or are the quotes note displaying today?

Data

Rhythmer, if your posts are being deleted it is because you have not read the forum guidelines! Answering questions for people is not the purpose in the homework forums; The idea is to get them to do at least a significant portion of the work on their own, so that they can actually learn to understand the material.

Guidelines: http://physicsforums.com/showthread.php?t=94379

cristo

As data mentions above, any and all questions which are coursework/homework type questions (regardless of whether the homework is set to be handed in) must be answered in a tutorial type way. That means, waiting for the original poster to show some work before giving help, and providing hints or suggestions as opposed to complete solutions.

Well, cristo would follow Halls' hint, using Hootenanny's formula for the distance, and then set them equal.