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QCE Maths Methods Questions Thread
snr.mmorris4.19:
whats the process behind solving these? Never seen them before i'm not sure where to start
P is a movable point on the line y=7-x
Find the coordinates of P when it is closest to the origin (0,0).
keltingmeith:
--- Quote from: snr.mmorris4.19 on September 15, 2020, 06:07:31 pm ---whats the process behind solving these? Never seen them before i'm not sure where to start
P is a movable point on the line y=7-x
Find the coordinates of P when it is closest to the origin (0,0).
--- End quote ---
This is a really interesting question! What I'm going to do is give you some starting points, then why don't you let us know how far you get?
Firstly, you may remember that the straight-line distance between any two points is given by the equation:
which is secretly just Pythagoras' theorem in disguise. Because you don't know the exact points of P, you could actually pretend that it lies on the point x_2=x and y_2=y.
Another thing to think about is that closest and furthest have some synonyms that would normally raise alarm bells to any student studying differentiation - maybe you can use differentiation in some way, here?
EDIT: See below for some pointers on using a non-calculus approach - I tried to generalise for other curves, not just for straight lines, but their approach is WAY simpler and still worth knowing. Particularly if you're not up to differentiation, yet
fun_jirachi:
In general, the shortest distance from a point to a line will be mapped by a line through the point and the line such that the two lines are perpendicular. For curves, we use the same idea but choose a line through the point and the curve such that the line is perpendicular to the tangent at the point of intersection (for further application that I'm certain will come up at some point down the line). Other problems similar to this are called locus problems - you might want to have a further look at these (there are all sorts, but they can all be more or less divvied up reasonably distinctly).
There are multiple ways of solving this - the two I'd recommend you have a look at are a) using the perpendicular distance formula or b) finding a perpendicular line passing through the given point, then finding the point of intersection to determine the coordinates of P. Expressing the distance as a polynomial function to exploit it as a max/min problem seems excessive for a question that involves a point and a line, but is worth exploring as suggested by keltingmeith as it will provide practice for tougher locus problems :)
EDIT: beaten by keltingmeith
orla007:
Hi :)
I would love some help with this question.
Thanks in advance
dzach0:
I have just finished year 10 and got a very unhappy mark for my methods exam (D+). I feel like it is due to me switching from general midway through the year and not being able to keep up with the pace. I want to get ahead on the topics for year 11 so that I am very confident in what I do. However I do not understand what I need to specifically revise on as the unit outlines only consist of hard to understand learning goals.
Does anyone know what specific topics and subtopics I have to revise for unit 1 at least? (I have attached the unit outlines given by my school)
Happy Holidays!
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