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I have this question and I am stuck as how to answer it. "Points A,B and C lie on a straight line. Point A has coordinates(1,p), point B has coordinates (q,9) and point C has the coordinates (r,15). Point B is the midpoint of AC. The distance between A and B is 6.5 " I understand that the distance between A and C is 13, and that I will probably need to use the midpoint equation and the distance equation, but how? Thanks.

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3 Answers 3

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$B$ being the midpoint of $AC$ means, in particular, its $y$ coordinate is the "midpoint" between the $y$ coordinates of $A$ and $C$. This should allow you to compute $p$. Then the distance between $A$ and $B$ should let you find $q$. Finally, with $p$ and $q$ in hand, you find $r$ the same way you found $p$.

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Hint by distance formula you have relation between $(p,r),(r,q),(p,q)$ and midpoint gives relation of $(p,q) with r $ that is $r=...p,r=...q$ if all is in r can you find $p,q,r$

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Hint: A, B, C form the hypothenuse of a right angle triangle where y = 15 and x = 1 are the other two sides, if you wanted another way to approach this question.

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    $\begingroup$ Huh? How can three points that LIE ON A STRAIGHT LINE for a right angle triangle? $\endgroup$
    – user325968
    Mar 30, 2016 at 11:09
  • $\begingroup$ I have clarified. $\endgroup$
    – Inazuma
    Mar 30, 2016 at 11:12

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