Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    16
    ReputationRep:
    The points A(-2, 3) and C(9, 4) are two vertices of an isosceles triangle ABC in which AC = BC. The side AB lies on x+y=1. Find coordinates of B.

    I’ve tried so much - I’ve worked out the length of AC and got root122, worked out the equation of AC as 11y=x+35. I’ve also tried letting B be (a,b) and working out an equation for the line BC and finding the equation where x+y=1 intersects this.

    Am I missing something?
    Offline

    9
    ReputationRep:
    (Original post by danielwinstanley)
    The points A(-2, 3) and C(9, 4) are two vertices of an isosceles triangle ABC in which AC = BC. The side AB lies on x+y=1. Find coordinates of B.

    I’ve tried so much - I’ve worked out the length of AC and got root122, worked out the equation of AC as 11y=x+35. I’ve also tried letting B be (a,b) and working out an equation for the line BC and finding the equation where x+y=1 intersects this.

    Am I missing something?
    Because B lies on x + y = 1, you can write its coordinates as (x, 1 - x).

    You know the distance AC, which you have worked out correctly.

    You know the distance BC is the same as this. Write an equation for the distance BC using the above version of the coordinates of B, and see there that gets you.
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by Pangol)
    Because B lies on x + y = 1, you can write its coordinates as (x, 1 - x).

    You know the distance AC, which you have worked out correctly.

    You know the distance BC is the same as this. Write an equation for the distance BC using the above version of the coordinates of B, and see there that gets you.
    So
    CB^2 = ((4-(1-x))^2 + (9-x)^2
    CB^2 = (x+3)^2 + (9-x)^2
    CB^2= 2x^2-12x+90

    Then there would I go from here? Would I make the quadratic equal to 122 and solve?

    Thanks
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    9
    ReputationRep:
    (Original post by danielwinstanley)
    So
    CB^2 = ((4-(1-x))^2 + (9-x)^2
    CB^2 = (x+3)^2 + (9-x)^2
    CB^2= 2x^2-12x+90

    Then there would I go from here? Would I make the quadratic equal to 122 and solve?

    Thanks
    Yes!
    • Thread Starter
    Offline

    16
    ReputationRep:
    (Original post by Pangol)
    Yes!
    Thanks so much
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.