Author Topic: As level Pure mathematics Question  (Read 1978 times)

Offline xxemoxx

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As level Pure mathematics Question
« on: August 28, 2009, 06:29:25 pm »
Show that the triangle formed by the points (-2,5) , (1,3) , (5,9) is right angled..

Please help
thanks its urgent

Offline astarmathsandphysics

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Re: As level Pure mathematics Question
« Reply #1 on: August 28, 2009, 07:20:03 pm »
Show that the triangle formed by the points (-2,5) , (1,3) , (5,9) is right angled..

Please help
thanks its urgent

Call the points A,B,C then AB=B-A=(3,-2) and AC=C-A=(7,4) and BC=C-B=(4,6)

dot product AB with BC=3*4+-2*6=0 there AB is at right angles to BC with a right angle at B
=

Offline xxemoxx

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Re: As level Pure mathematics Question
« Reply #2 on: August 28, 2009, 07:54:36 pm »
thankyou! I slved that Q sometime back
can u help me with this one..
A(7,2) C(1,4) are two vertices of a square ABCD
(a)find the equation of the diagonol BD
(b) Find the coordinates of B and of D

Offline astarmathsandphysics

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Re: As level Pure mathematics Question
« Reply #3 on: August 30, 2009, 10:37:44 am »
thanks

Offline spiderman

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Re: As level Pure mathematics Question
« Reply #4 on: September 03, 2009, 11:53:05 am »
sin(2@+60)=0.3584
find the least 2 +ve values of @...



Pls someone help me.......in solving d sum
Always hangin around ur neighbourhood..........

nid404

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Re: As level Pure mathematics Question
« Reply #5 on: September 03, 2009, 02:59:00 pm »
sin(2@+60)=0.3584
find the least 2 +ve values of @...



Pls someone help me.......in solving d sum

this one's a litlle tricky but you can't be fooled by these cie crappy ppl

here u go
sin(2 theta + 60)=0.3584
so
2 theta+60=sin-10.3584
2 theta+60=21.0019...
now comes the part....u know ull get  negative answer if u use this value of the inverse
so u take 180-21.0019 and theta + 360 cuz these also have value of inverse is 0.3584 (translation and periodic property)
i hope u got this part
so then,
2 theta+60=158.998...
2 theta= 158.998...-60
theta=49.5
and then
2 theta+60=381.001967...
2 theta= 381.001967-60
theta= 160.5




Offline astarmathsandphysics

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Re: As level Pure mathematics Question
« Reply #6 on: September 27, 2009, 08:35:57 pm »
thankyou! I slved that Q sometime back
can u help me with this one..
A(7,2) C(1,4) are two vertices of a square ABCD
(a)find the equation of the diagonol BD
(b) Find the coordinates of B and of D
gradient of AC=(4-2)/(1-7)=-1/3
so gradient of perpendicular line=-1/(-1/3)=3
Also the mid point of AC is a point on BD. Mid point of AC=((7+1)/2,(2+4)/2)=(4,3)
Equation of BD is y=3x+c sub (4,3) in to find c
3=3*4+c so c=-9 and y=3x-9 is equation of BD.

the vector from A to C=(-6,2) so the vector from the midpoint is (-3,1) hence since BD is perpendicular the vector from the centre to eith B or D is (1,3) hence the coordinates are (4,3)+(1,3)=(5,6) or (4,3)-(1,3)=(3,0)
« Last Edit: September 27, 2009, 08:55:43 pm by astarmathsandphysics »

Offline Ghost Of Highbury

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Re: As level Pure mathematics Question
« Reply #7 on: February 11, 2010, 06:18:45 pm »
gradient of AC=(4-2)/(1-7)=-1/3
so gradient of perpendicular line=-1/(-1/3)=3
Also the mid point of AC is a point on BD. Mid point of AC=((7+1)/2,(2+4)/2)=(4,3)
Equation of BD is y=3x+c sub (4,3) in to find c
3=3*4+c so c=-9 and y=3x-9 is equation of BD.

the vector from A to C=(-6,2) so the vector from the midpoint is (-3,1) hence since BD is perpendicular the vector from the centre to eith B or D is (1,3) hence the coordinates are (4,3)+(1,3)=(5,6) or (4,3)-(1,3)=(3,0)


sir, wat is this concept named as? i mean, wat is the rule u applied in ur last sentence called?
divine intervention!

Offline astarmathsandphysics

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Re: As level Pure mathematics Question
« Reply #8 on: February 11, 2010, 06:25:30 pm »
Can you quote the part you arequerying

Offline Ghost Of Highbury

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Re: As level Pure mathematics Question
« Reply #9 on: February 11, 2010, 06:27:44 pm »
the vector from A to C=(-6,2) so the vector from the midpoint is (-3,1) hence since BD is perpendicular the vector from the centre to eith B or D is (1,3) hence the coordinates are (4,3)+(1,3)=(5,6) or (4,3)-(1,3)=(3,0)


the above, wat is the concept called? the concept which states abt the sign switching and vectors..just wanted to know so i can look it up and learn it.! plz help
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Offline astarmathsandphysics

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Re: As level Pure mathematics Question
« Reply #10 on: February 11, 2010, 06:58:36 pm »
A vector which goes in the opposite direction has the opposite sign. There is not really a name to it.

Offline joel

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Re: As level Pure mathematics Question
« Reply #11 on: April 11, 2010, 04:42:59 pm »
Easy find all the lengths of sides and do
 
c^2 = a^2 + b^2

taking c as the longest side