Midpoint
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hey guys how do you find midpoint of 2 points without using the formula
(x1+x2)/2, (y1+y2)/2
say point A(2,4), and point B(3,6)
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so how do you find the midpoint w/o using the formula stated above?
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Originally posted by Divanhot:
hey guys how do you find midpoint of 2 points without using the formula
(x1+x2)/2, (y1+y2)/2
say point A(2,4), and point B(3,6)
Why don't use the formula? If you don't want use, go plot it out lo
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tts e easiest way liao my dear
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y = mx + c?
(y - 4) = 2 (x - 2)
y = 2x
x = 2.5, y = 5
it's still easier to use midpoint formula.
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Originally posted by Divanhot:
hey guys how do you find midpoint of 2 points without using the formula
(x1+x2)/2, (y1+y2)/2
say point A(2,4), and point B(3,6)
TS, when the "O" level examiners say that mid-point formula is excluded in the
new syllabus "O" level E.Maths, this means that the mid-point concept and formula
will not be tested.
If you are a government student, you can easily check it with your teacher.
If you are a tutor, please read the detailed syllabus at MOE SEAB website.
Alternatively, you can check the latest edition "O" level Mathematics Textbooks
used in the government schools, the mid-point concept and formula are no longer
tested at "O" level E.Maths.
Mid-point concept and formula has been shifted to the new syllabus "O" level
Additional Mathematics.
For your information, the mid-point of 2 points is best understood
by joining the 2 points by a line and the mid-point is at the half length of the line.
The mid-point is found by reading the x-ordinate and y-ordinate at the half length
point.
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y = 2x ----------- (1)
y = -2x + 10 ----(2)
2x = -2x + 10
4x = 10
x = 2.5
therefore y = 5
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Originally posted by Divanhot:
hey guys how do you find midpoint of 2 points without using the formula
(x1+x2)/2, (y1+y2)/2
say point A(2,4), and point B(3,6)
Simple. Use vector. For point A and B. Assume M = midpoint
vec(AM)=vec(MB)
vec(AO)+vec(OM)=vec(MO)+vec(OB)
2[vec(OM)]=vec(OB)+vec(OA)
vec(OM) =0.5[vec(OB)+vec(OA)]
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Originally posted by deepak.c:
y = 2x ----------- (1)
y = -2x + 10 ----(2)
2x = -2x + 10
4x = 10
x = 2.5
therefore y = 5
hi bro, how do u get y= -2x +10?
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i found the solution after sometime :)
do refer to this diagram for easier understanding: http://img199.imageshack.us/i/midpt.jpg/
let's consider a new set of pts A(1,1), pt B(3,6): Distance AB= square root of 29 let M be the midpt of AB.
Distance AM=BM= (square root of 29)/2
consider AM: (x-1)^2 + (y-1)^2 = 29/4 (x^2-2x+1)+ (y^2-2y+1)= 29/4--> equation (1)
consider MB: (3-x)^2+(6-y)^2= 29/4 (9-6x + x^2)+ (36-12y+y^2)= 29/4--> equation (2)
since AM= BM, equation (1)= equation (2)
4x+ 10y= 43---> equation (3)
now consider tan alpha and tan beta
tan alpha= (y-1)/(x-1), tan beta= (6-y)/(3-x)
tan alpha= tan beta( corresponding angles)
(y-1)/(x-1) = (6-y)/(3-x)
2y-5x= -3 --> equation (4)
subst x= (43-10y)/4 into equation (4): y= 3.5.
subst y=3.5 into eqn (3), x= 2 Hence Midpt is (2,3.5)
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TS, you seems to be very keen in maths.
How many ways can we find the value of square root of 9704 ?
Please do not use the calculator to find the square root of 9704.
How many other ways are there to find the square root of 9704 ?
How do ancient Chinese Mathematicians find the value ?
How do mathematicians before the invention of calculator find the value ?
How to find the value of tan 36.7, sin 45.8, cos 23.9 ?
Please do not use the calculator (and mathematical tables and slide ruler) to find
these values.
How can we find these values manually ?
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Originally posted by Divanhot:
hey guys how do you find midpoint of 2 points without using the formula
(x1+x2)/2, (y1+y2)/2
say point A(2,4), and point B(3,6)
Alternative solution:
Let midpoint of point A & B be M ==> AM = BM
Magnitude of line AM = sqrt(5) / 2
Equation of line AB: y = 2x
[ (x-2)^2 + (y-4)^2] ^ (1/2) = (5/4) ^ (1/2) -------------------------------- <1>
sub y = 2x into <1>,
solve x = 3/2 (N.A) or 5/2
Therefore, x = 2.5, y = 5
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Originally posted by Divanhot:
I just swapped the 2 points around, y from point A becomes y in point B.
(2, 6) and (3, 4).
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Still... the formula works better....
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Originally posted by lianamaster:
Still... the formula works better....
Me also like that say.
