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Question 404284: the coordinate of the midpoint of the line joining A(p²,p)and B(q²,q) are (5,1) find the possible values of p and q
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the coordinate of the midpoint of the line joining A(p²,p)and B(q²,q) are (5,1) find the possible values of p and q
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Equations:
(p^2+q^2)/2 = 5
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(p+q)/2 = 1
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Modify:
p^2+q^2 = 10
p + q = 2
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Substitute for "p" and solve for "q":
(2-q)^2+q^2 = 10
4-4q+2q^2 = 10
2q^2-4q-6 = 0
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2q^2-6q+2q-6 = 0
2q(q-3)+2(q-3) = 0
(q-3)(2q+2) = 0
q = 3 or q = -1
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Solve for "p":
If q = 3
Since p+q = 2
p = 2-q = -1
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If q = -1
Since p+q = 2
p = 3
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Cheers,
Stan H.
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