Point P (5,-3) is one of the two points of trisection of the line segment joining the points A (7,-2) and B (1, -5) near to A. Find the co-ordinates of the other point of trisection.
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A(7,-2) and B(1,-5)
AP=1=m (given)
PB=2=n (given)
Let the unknown co-ordinate be Q(x,y)
Now,Section Formula:
mx₁+nx₂ my₁+ny₂
Q(x,y)= ----------- , ₋₋₋₋₋₋₋₋₋₋
m+n m+n
So.
1(7)+2(1) 1(-2)+2(-5)
------------- , -----------------
1+2 1+2
Now,
x=9/3=3 &
y=-12/3=-4
∴ x=3 and y=-4.
AP=1=m (given)
PB=2=n (given)
Let the unknown co-ordinate be Q(x,y)
Now,Section Formula:
mx₁+nx₂ my₁+ny₂
Q(x,y)= ----------- , ₋₋₋₋₋₋₋₋₋₋
m+n m+n
So.
1(7)+2(1) 1(-2)+2(-5)
------------- , -----------------
1+2 1+2
Now,
x=9/3=3 &
y=-12/3=-4
∴ x=3 and y=-4.
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