February 13th, 2018, 09:37 AM  #1 
Newbie Joined: Feb 2018 From: Iran Posts: 7 Thanks: 0  Analytic of point
If the area of triangle ABC with the vertices A(3,1) B(1,2) and C(m,1) is five square units find the possible values of m?

February 13th, 2018, 10:51 AM  #2 
Newbie Joined: Dec 2017 From: Spain Posts: 13 Thanks: 0 
Drawing that in a coordinatesystem, you might notice that the point C has to lie on the function f(x)=1. The altitude to the side AC equals 3 units (=1(2)). Hence (using area formula: h(c)*c/2) we get: 5=c*3/2 $\ \ \ \ \ \ \ $ /*(2/3) 10/3=c Now, remember that the triangle ABC can also be obtuse. Thus the point C lies on (19/31) or (1/31). (You either subtract 10/3 from 3 or add it). We finally have: m(1)=19/3≈6,3 m(2)=1/3≈0,3 Last edited by skipjack; February 13th, 2018 at 06:28 PM. 

Tags 
analytic, point 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Point on a line segment closest to another point  weesam  Geometry  13  October 25th, 2015 04:37 PM 
Nearest distance from point to point on line  abcdefgh123  Algebra  2  January 4th, 2014 04:08 PM 
Drawing a line from point a,b .. coords point b unkown  Vibonacci  Algebra  5  September 17th, 2012 01:28 AM 
analytic, fixed point  eskimo343  Complex Analysis  3  February 24th, 2010 05:07 PM 
calculating point of line given starting point, slope  mathsiseverything  Algebra  1  March 4th, 2008 07:41 AM 