Question 176789
Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ
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Plot the points.
Let PQ be the hypotenuse of a rt. triangle with 3rd point R(7,3)
Find length of PQ: sqrt(8^2+2^2) = sqrt(68) = 2sqrt(17)
(1/4)2sqrt(17) = (1/2)sqrt(17)
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let a point (1/4)th of the way from P to Q be M(x,y)
Draw a line segment from M perpendicular to PR at N.
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Triangle PMN is proportional to Triangle PQR.
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A point (1/4) of the way from P to R is (1,3)
A point (1/4) of the way from R to Q is (7,3 1/2)
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so the point (1/4) of the way from P to Q is (1,(7/2))
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Prove it:
distance from P to Q = sqrt[(1--1)^2 + (3-(7/2)^2] = sqrt[4 + 1/4] 
= sqrt[17/4] = (1/2)sqrt(17)
and this is (1/4) the way from P to Q.
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Cheers,
Stan H.