# geometry

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A 30-lb child is siting at A(2,3) and a 50-lb child is at B(12,7) where units are feet .Find the point P between A and B which could be used as the fulcrum of a teeter board putting the two children in equilibrium.
30 AP=50 PB or (AP/PB)=5/3

• geometry -

A(2,3), P(x,y), B(12,7).

30AP = 50BP,
AP = (5/3)BP,
x - 2 = 5/3(12-x),
Multiply both sides by 3:
3x - 6 = 5(12-x),
3x - 6 = 60 - 5x,
3x + 5x = 60 + 6,
8x = 66,
X = 8 2/8 = 8 1/4.

y- 3 = 5/3(7-y),
Multiply both sides by 3:
3y - 9 = 5(7-y),
3y - 9 = 35 - 5y,
3y + 5y = 35 + 9 ,
8y = 44,
Y = 5 4/8 = 5 1/2.

Solution set: P(8 1/4,5 1/2).

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