Locus Question 0.0 (1 Viewer)

[kev-kun]

This question is just throwing me off. Part ii asks to find the area of the triangle.... No idea on how to go about it. Help is much appreciated!

 

[HSC2014]

Ah, finally worked it out; ending was a little tricky.
Start with what you know about triangles: How do you find the area of one? Which method seems most suitable to your question? Then go for it.

 

[kev-kun]

hmmm... either the basic 1/2bh or trig but there's no angle. So the most appropriate is the basic one... hmmm. Base is probably PQ but perpendicular height not sure...

 

[HSC2014]

Trust your gut instinct. If you want to excel in higher level math, you have to develop insight - and that is only achievable through experience and fault. As for base, it can be anything in a triangle, depending on perspective. The only question here is which is most efficient for the algebra.

 

[HeroicPandas]

There is a reason why they wrote the equation of PQ to be like that instead of

 

[kev-kun]

OMG I figured it out =='' Haha Thanks for the advise, good inspiration.

 

[SharkeyBoy]

Point O to line PQ is obtained via perp. dist. formula
PQ can be found using distance formula.
Then just 1/2bh

 

[HSC2014]

That's okay When in doubt, go back to your foundations and use the tools you've learnt in mathematics.

 

[RealiseNothing]

A much easier approach:

Drop perpendiculars from the points P and Q to the x-axis and make them the points P' and Q' respectively. So now you have a trapezium PP'Q'Q.

Now Area of OPQ = Area of PP'Q'Q - Area of OPP' - Area of OQQ'







Therefore by subtracting the area of the two triangles from the trapezium we get:

 

[RealiseNothing]

A diagram to show what I mean:

 

[Drongoski]

OMG I figured it out =='' Haha Thanks for the advice, good inspiration.

*

 

[Drongoski]

A much easier approach:

Drop perpendiculars from the points P and Q to the x-axis and make them the points P' and Q' respectively. So now you have a trapezium PP'Q'Q.

Now Area of OPQ = Area of PP'Q'Q - Area of OPP' - Area of OQQ'







Therefore by subtracting the area of the two triangles from the trapezium we get:

Nice effort & the diagram too.