If the centroid of the triangle formed
by (p,q), ( 9,1), (1,p) is the origin, then
p + q3+1 =
Answers
Step-by-step explanation:
Given :-
The centroid of the triangle formed by (p,q), ( 9,1), (1,p) is the origin.
To find :-
Find the value of p + q^3+1 ?
Solution:-
Given points are :(p,q), ( 9,1), (1,p)
Let (x1, y1)=(p,q)=>x1=p and y1 = q
Let (x2, y2)=(9,1)=> x2=9 and y2=1
Let(x3, y3)=(1,p)=>x3=1 and y3=p
We know that
The centroid of a triangle formed by the three vertices A(x1, y1) ,B(x2, y2) and
C(x3, y3) is G(x,y)
=( {x1+x2+x3}/3 ,{y1+y2+y3}/3 )
On Substituting these values in the above formula then
=> ( {p+9+1}/3 , {q+1+p}/3 )
=> ( {p+10}/3 , {p+q+1}/3 )
According to the given problem
The centroid of the given points is the origin
The coordinates of the Origin = (0,0)
=> ( {p+10}/3 , {p+q+1}/3 ) = (0,0)
On Comparing both sides then
=> (p+10)/3 = 0 and (p+q+1)/3 = 0
=> p+10 = 0×3 and p+q+1 = 0×3
=> p+10 = 0 and p+q+1 = 0
=> p = -10 and p+q+1 = 0
We have p = -10
now
p+q+1 = 0
=> -10+q+1 = 0
=> -9+q = 0
=> q = 9
Now
p+q^3+1
=> -10+9^3+1
=> -10+729+1
=> -10+730
=> 720
Answer:-
The value of p = -10
The value of q = 9
The value of p+q+1 = 0
The value of p+q^3+1 = 720
Used formulae:-
The centroid of a triangle formed by the three vertices A(x1, y1) ,B(x2, y2) and C(x3, y3) is G(x,y)
=( {x1+x2+x3}/3 ,{y1+y2+y3}/3 )
Step-by-step explanation:
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