Finding a Point Equidistant From Two Other PointsDate: 8/18/96 at 17:5:44 From: Anonymous Subject: Finding a Point Equidistant From Two Other Points Point A is (-5,-3), and point B is (-1,-5). What should the value of k be for the point (3, k) to be equidistant from A and B? I tried to use the distance formula for this problem but I couldn't solve for k that way. What should I do? A very confused Jason. Date: 8/30/96 at 15:26:47 From: Doctor Jerry Subject: Re: Finding a Point Equidistant From Two Other Points If the distance from (3,k) to A and B is equal, then the squares of the distances from (3,k) to A and B are also equal. This will simplify the calculations. From (3,k) to (-5,-3), the square of the distance is 64+(k+3)^2. From (3,k) to (-1,-5), the square of the distance is 16+(k+5)^2. Setting these expressions equal, 64+(k+3)^2 = 16 +(k+5)^2 squaring, 64+k^2+6k+9 = 16+k^2+10k+25 simplifying, 4k = 32 So, k = 8. Now check the squared distances. From (3,8) to (-5,-3) is 64+121 = 185. From (3,8) to (-1,-5) is 16+169 = 185. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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