How to find endpoint when given and endpoint, and midpoint?
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Ex endpoint: (10,12) (6,9) how to find the other endpoint pleasee show work.
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Answer:
ok so (im assuming that the 2nd coordinate pair is the midpoint) the variables for the pairs will be expressed as follows: (10,12) = (x1,y1) (6,9) is the midpoint, so it does not have numerical "tagging," if you will.) usually the numbers look like exponents but after the letter towards the bottom of it, so they will be placed after the variable as regular numbers because this a computer and I don't have the capability to write it like the book does. so anyway, the midpoint formula is as follows: m= ((x1+x2)/2, (x2+y2)) m is the midpoint, and each number after the variable simply represents which pair it is from. so now, plug the points into the formula, remember that the midpoint pair goes in place of the m, and the x value of the endpoint goes in place of x1, while the y value goes in place of y1, so the second enpoint is represented by (x2, y2): (6,9) = ((10+x2)/2 , (12+y2)/2) so now, distribute the denominators as follows: (6,9) = ((10/2)+((x2)/2) , (12/2)+((y2)/2)) and now simplify as follows: (6,9) = (5+ (x2)/2 , 6+(y2)/2) now treat each coordinate value in separate equations as follows: 6 = 5+ (x2)/2 9 = 6+ (y2)/2 and solve each equation as follows: 1 = (x2)/2 x2 = 2 3 = (y2)/2 y2 = 6 so there, you have two coordinate values. so therefore, your other endpoint is (2,6). if you would like to check your work, just plug the numbers into the equation so that both sides of the equation or equal, as follows: (6,9) = ((10+2)/2 , (12+6)/2) (6,9) = (12/2 , 18/2) (6,9) = (6,9) hope this helps!! :) xoxo
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