# SOLUTION: Can you find the coordinates of B given A(3,8) and M(5,4)? M is the midpoint of. Graph: A-----M-----B

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 Click here to see ALL problems on Linear Algebra Question 319054: Can you find the coordinates of B given A(3,8) and M(5,4)? M is the midpoint of. Graph: A-----M-----B Answer by Edwin McCravy(9717)   (Show Source): You can put this solution on YOUR website!Can you find the coordinates of B given A(3,8) and M(5,4)? M is the midpoint of. ``` There are two ways. We'll do both. Graphically: Draw the right triangle with one leg vertical and one leg horizontal that has AM as its hypotenuse: Notice that the vertical leg is 4 units and the horizontal leg is 2 units long. So duplicate that triangle below, and you have this, so you see that M(5,4) is the midpoint between A(3,8) and B(7,0). Second way: Let B have the coordinates B(, ) Then use the midpoint formula: Midpoint between (,) and (, ) is = (5,4) Let A(3,8) = (,) so that , and Let B have the coordinates B(, ) Then and So you have the system of equations Multiply both equations through by 2 Solve each and get: So M(5,4) is the midpoint between A(3,8) and B(7,0). Do it whichever way your teacher wants. Edwin```