# SOLUTION: 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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 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 PQFound 2 solutions by Alan3354, stanbon:Answer by Alan3354(30993)   (Show Source): You can put this solution on YOUR website! 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 ------------------- Calculate x and y separately. diff in x = (7 - (-1)) = 8 diff in y = (5-3) = 2 1/4 of x = 2 1/4 of y = 1/2 Call the point R Rx = Px + 2 = +1 Ry = Py + 0.5 = 3.5 So R is: (1,3.5) Answer by stanbon(57290)   (Show Source): You can put this solution on YOUR website!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 ------------------------------------- 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) ----------------------------------- 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. -------------- Triangle PMN is proportional to Triangle PQR. ----- 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) ------------------ so the point (1/4) of the way from P to Q is (1,(7/2)) ------------------ 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. =========================================== Cheers, Stan H.