Question
If in triangle 
, circumcenter 
and orthocenter 
then the co-ordinates of mid-point of side opposite to is :
- (1, -11/3)
- (1,5)
- (1, -3)
- (1,6)
Hint:
Centroid, orthocenter, circumcenter are collinear. The centroid divides the median in 2:1 ratio.
The correct answer is: (1, -11/3)
Given That:
If in triangle , circumcenter and orthocenter then the co-ordinates of mid-point of side opposite to is :
>>>The orthocenter, centroid and circumcenter of any triangle are collinear. And the centroid divides the distance from orthocenter to circumcenter in the ratio 2:1.
>>Let the centroid be G(x, y) , its coordinates can be found using the section formula. Then,
>>> Also, the centroid (G) divides the medians (AD) in the ratio 2:1. Then:
>>>Let the coordinates of D be (h, k)
h=1 and 6k+30=8
and k = 
∴D(h, k)=(1,)
)>>> The orthocenter, centroid and circumcenter of any triangle are collinear. And the centroid divides the distance from orthocenter to circumcenter in the ratio 2:1.
>>> Also, the centroid (G) divides the medians (AD) in the ratio 2:1.
>>> ∴D(h, k)=(1,)
Related Questions to study
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If the point 
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>>> L11 
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>>> (1+cos
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If 
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If be any point on a line then the range of for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is
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is any point in the interior of the quadrilateral formed by the pair of lines and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is
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>>> ( a - 2 )( a - 4 ) < 0
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Assertion (A): The lines represented by 
and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)
Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.
Assertion (A): The lines represented by and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)
Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.
In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:
In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:
P1,P2,P3, be the product of perpendiculars from (0,0) to 
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P1 = 1;
P2 = 
;
P3 = 
;
>>> Therefore, we can say that P1>P2>P3.
P1,P2,P3, be the product of perpendiculars from (0,0) to respectively then:
P1 = 1;
P2 = ;
P3 = ;
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If θ is angle between pair of lines 
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>>> 
= 2.
>>> tan = 
>>> 
= 10.
If θ is angle between pair of lines , then
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>>> tan =
>>> = 10.
If the pair of lines 
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If the pair of lines intersect on the x-axis, then 2fgh=
If the pair of lines intersect on the x-axis, then ac=
If the pair of lines intersect on the x-axis, then ac=
If the equation 
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If the equation represents a pair of perpendicular lines then its point of intersection is
If the lines 
and 
are concurrent then λ
>>> The value of is 2.
If the lines and are concurrent then λ
>>> The value of is 2.
