# 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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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 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```
The text passage contains a geometric proof question and its solution, involving the proof that a segment is the perpendicular bisector of another segment in a triangle.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 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```
user
The text passage contains a geometric proof question and its solution, involving the proof that a segment is the perpendicular bisector of another segment in a triangle.

TYPE: SINGLE_QUESTION_WITH_ANSWER