Asked by Sal
                The points A,B,C,D have coordinates (3,3) (8,0) (-1,1) (-6,4) respectively.
Find the coordinates of the point of intersection of the diagonals AC and BD?
Help plZ!!!
            
        Find the coordinates of the point of intersection of the diagonals AC and BD?
Help plZ!!!
Answers
                    Answered by
            Reiny
            
    You will have to find the equation of both diagonals
I will do AC , using the points (3,3) and (-1,1)
slope of AC = (3-1)/(3+1) = 2/4 = 1/2
then again using (3,3)
y-3 = (1/2)(x-3)
2y - 6 = x-3
<b>x - 2y = -3</b>
Now you find the equation for BD
then solve the two equations.
    
I will do AC , using the points (3,3) and (-1,1)
slope of AC = (3-1)/(3+1) = 2/4 = 1/2
then again using (3,3)
y-3 = (1/2)(x-3)
2y - 6 = x-3
<b>x - 2y = -3</b>
Now you find the equation for BD
then solve the two equations.
                    Answered by
            Sal
            
    I get the gradient part reiny, but how do you use one of  the points to get the equation?
    
                    Answered by
            Sal
            
    The gradient/slope for BD is -2/7
    
                    Answered by
            Sal
            
    Ah wait i got the equation for BD as 
y=-2/7 x + 16/7
is that right?
    
y=-2/7 x + 16/7
is that right?
                    Answered by
            Reiny
            
    Maybe you use y = mx + b
then y = (1/2)x + b
sub in (3,3)
3 = (1/2)(3) + b
b = 3 - 3/2
b = 3/2
y = (1/2)x + 3/2
suppose I multiply each term by 2 to get
2y = x + 3
re-arrange for x - 2y = -3 , the same as I had before, but much easier and faster
The method of y = mx + b seems to be the one taught most often these days, but personally, I would hardly ever use it if my slope is a fraction.
If the slope is an integer, then it makes sense to use
y = mx + b
    
then y = (1/2)x + b
sub in (3,3)
3 = (1/2)(3) + b
b = 3 - 3/2
b = 3/2
y = (1/2)x + 3/2
suppose I multiply each term by 2 to get
2y = x + 3
re-arrange for x - 2y = -3 , the same as I had before, but much easier and faster
The method of y = mx + b seems to be the one taught most often these days, but personally, I would hardly ever use it if my slope is a fraction.
If the slope is an integer, then it makes sense to use
y = mx + b
                    Answered by
            Reiny
            
    Yes, your second equation is correct
    
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