A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 4 years ago

A diagram showing a trapezium ABCD in which AD is paralel to BC and AB is perpendicular to BC and AD. The coordinates of A, B, C are (-2,5), (3,9),(7,4) respectively. AD cuts the x-axis at E. Given further that AE:ED is 2:3 and AE=BC, find the coordinates of D.

  • This Question is Closed
  1. dumbcow
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    D = (8,-7.5) slope of AB is 4/5, therefore the perpendicular slope of AD is -5/4 using point A (-2,5) the line connecting A to D: y = -5/4x + 5/2 the x-intercept can be found by plugging in 0 for y x = 2, therefore point E =(2,0) AE =BC = sqrt(41) using the given ratio: sqrt(41)/ED = 2/3 --> ED = 3sqrt(41)/2 Use the distance formula to find point D (x,y) sqrt[(x-2)^2 +y^2] = 3sqrt(41)/2 substitute in for y sqrt[(x-2)^2 +(-5/4x + 5/2)^2] = 3sqrt(41)/2 (x-2)^2 +(-5/4x + 5/2)^2 = 92.25 expand and simplify --> x^2 -4x -32 = 0 (x-8)(x+4) = 0 x = 8, x can't be -4 because of the direction of line AD plug it into equation of line to find y y = -5/4(8) +5/2 = -7.5

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.