August 30th, 2018, 12:35 PM  #1 
Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2  Coordinate geometry
A square ABCD has its diagonal AC and BD lying along the lines 3x7y25=0 7x+3y10=0 respectively The side CD lies along the line 2x+5y7=0 1. Calculate the coordinates of the triangle ACD 2. Obtain the equation of the line AB 3. Find the perimeter of ACD I have tried substituting equ. of line1 from 2, but that does not work. I need all possible aid.... Please. Last edited by skipjack; August 30th, 2018 at 02:13 PM. 
August 30th, 2018, 01:04 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,766 Thanks: 697 
1. and 3. give you point C, 2. and 3. give you point D. This gives you one side. Now you can graph it. See if you can do the rest.

August 31st, 2018, 05:37 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
As CD has slope 2/5, AD has slope 1/(2/5) = 5/2. This may assist in finding the coordinates of A. It's then easy to find the equation of AB. Solving 3x  7y  25 = 0 and 2x + 5y  7 = 0, as suggested by mathman, gives (x, y) = (6, 1). This is point C. Solving 7x + 3y  10 = 0 and 2x + 5y  7 = 0 gives x = y = 1, so D is the point (1, 1). Solving 3x  7y  25 = 0 and 7x + 3y  10 = 0 gives (x, y) = (5/2, 5/2) as the coordinates of where the diagonals of the square intersect. You don't need to know that point, but as it's the midpoint of both AC and BD, it's now very easy to find the coordinates of A and B. Specifically, A = 2(5/2, 5/2)  (6, 1) = (1, 4), and B = 2(5/2, 5/2)  (1, 1) = (4, 6). You now have the coordinates of every point referred to, so you have the coordinates of at least two points on each of the lines referred to. This article gives two ways of writing an equation of the line through two known points. 
August 31st, 2018, 06:29 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
 
September 1st, 2018, 09:15 PM  #5 
Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 
Help me, why did he multiply the coordinates of the midpoint by 2 before subtraction? That's not clear.
Last edited by skipjack; September 2nd, 2018 at 06:21 AM. 
September 2nd, 2018, 06:21 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
For any two points R and S, their midpoint M = (R + S)/2, so 2M = R + S. Hence subtracting either one of the original points from 2M gives the other one. 

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