text: # SOLUTION: Given: triangle ABC A(-1,2) B(7,0) C(1,-6) and a point D(4,-3) on segment BC Prove: segment AD is the perpendicular bisector of segment BC
  
  Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: Given: triangle ABC A(-1,2) B(7,0) C(1,-6) and a point D(4,-3) on segment BC Prove: segment AD is the perpendicular bisector of segment BC      Log On
  
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   Question 144172: Given: triangle ABC A(-1,2) B(7,0) C(1,-6) and a point D(4,-3) on segment BC Prove: segment AD is the perpendicular bisector of segment BCAnswer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!Given: triangle ABC A(-1,2) B(7,0) C(1,-6) and a point D(4,-3) on segment BC Prove: segment AD is the perpendicular bisector of segment BC ``` First we use the midpoint formula to show that D is the midpoint of BC. That will show that AD is a bisector of BC. Then we will use the slope formula to show that AD is perpendicular to BC. The midpoint of the segment joining (,) and (,) is given by the formula = (,) We use B(,) as (,) and C(,) as (,) = (,) = (,) = (,) = (,) Since D has those coordinates, AD bisects BC. Now we need to show AD and BC are perpendicular. The slope of the segment joining (,) and (,) is given by the formula So we now find the slope of BC, again using B(,) as (,) and C(,) as (,) So the slope of BC is Now So we now find the slope of AD, using A(,) as (,) and D(,) as (,) So the slope of AD is Since and are reciprocals with opposite signs, this proves AD is perpendicular to BC. Therefore AD is the perpendicular bisector of BC. Edwin```