SOLUTION: 1.A Triangle Has Vertices at A(3,2) B(4,0) C(8,2). a) Show the triangle is right angled b) Find the Co-ordinates of the Point D such that ABCD is a rectangle

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: 1.A Triangle Has Vertices at A(3,2) B(4,0) C(8,2). a) Show the triangle is right angled b) Find the Co-ordinates of the Point D such that ABCD is a rectangle      Log On

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Question 363854: 1.A Triangle Has Vertices at A(3,2) B(4,0) C(8,2).
a) Show the triangle is right angled
b) Find the Co-ordinates of the Point D such that ABCD is a rectangle
Answer by ewatrrr(10682) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

a. Show the triangle is right angled

mAB = -2/1  mBC = 2/4 = 1/2   

AB is perpendicular to BC as their slopes are negative reciprocals.

b.  Co-ordinates of the Point D such that ABCD is a rectangle

BC and AD would be parallel and have same slope = 1/2

y = 1/2x + b Using point (3,2) b = -1/2

y = .5x + .5 (red line) mCD = -2  CD meets AD at (7,4)