Turn on thread page Beta
    • Thread Starter

    At this moment of time I feel like strangling co-ordinative geometry
    but I dont think thats very realistic
    I am do pracitse questions and the mark scheme does not show how they got to the answer.
    So could you awesomely clever people show how they got these answers.

    The points A(1,7) B (20,7) C(15,-3) form the verticies of a triangle ABC, as shown in Figure 1. The point D (8,2) is the midpoint of AC

    The line l , which passes through D and is perpendicular to AC , interscets AB at E.
    a)find the equation for l , in the form ax+by+c=0 where a,b and c are intergers.
    b) Find the exact co-ordinates of e

    Thank you guys so much,

    positive rep for the one which is most helpful

    a) find the gradient of the line AD. then, find gradient of normal to this. then, use this and the coordinates of D to find the line
    b) find the equation of the line AB, and solve simultaneously with the solution of a)

    You can find the line through A and C by using the points themselves.

    You are then told that l is perpendicular (hint: what does this do to the gradient?) and that l passes through D so use these two facts to give your answer to a)

    For b), the question is merely "What is the point of intersection of l and AB?"

    Well first find the gradient of the line AC using the points of the triangle i.e.:

    Now if the line is perpendicular to AC then the gradients of AC and l multiplied together give -1. So you just divide -1 by the gradient of AC to get:

    This is the gradient of l. Now you know it passes through D. So use the formula for finding the equation of the line with only one point.

    Now simplify this into the form required in the question.
    For the next part work out the equation of the line of AB by working out its gradient and then using either A or B with the line formula in the C1 book(the one which only uses one point and the gradient). Solve simulataneously with the equation of l

    you can make it easier for yourself by drawing a diagram really.

    well, AC, of which lies midpoint, D, and is perpendicular to l1.
    so find gradient of AC, which is y2-y1/x2-x1. you should get -3-7/15-1. so -10/14.
    as l1 is perpendicular to D. get the reciprocal of gradient, so 14/10
    then put it into the equation y-y1=m(x-x1) where x1 and y1 are (8,2) as the line goes through it.


    in the form of ax+by+c=0

    and for b)

    you know that E must have y-coordinate of 7 as both A and B have y-coordinate of 7.

    so just sub y=7 into
    so, 1.4x-7-9.2=0

    so the coordinates of E are

    hope it helps
The home of Results and Clearing


people online now


students helped last year

University open days

  1. SAE Institute
    Animation, Audio, Film, Games, Music, Business, Web Further education
    Thu, 16 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Fri, 17 Aug '18
  3. University of Bolton
    Undergraduate Open Day Undergraduate
    Fri, 17 Aug '18
Do you want your parents to be with you when you collect your A-level results?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


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

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

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