Posted by Sal on .
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!!!

Geometry 
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 = (31)/(3+1) = 2/4 = 1/2
then again using (3,3)
y3 = (1/2)(x3)
2y  6 = x3
x  2y = 3
Now you find the equation for BD
then solve the two equations. 
Geometry 
Sal,
I get the gradient part reiny, but how do you use one of the points to get the equation?

Geometry 
Sal,
The gradient/slope for BD is 2/7

Geometry 
Sal,
Ah wait i got the equation for BD as
y=2/7 x + 16/7
is that right? 
Geometry 
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
rearrange 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 
Geometry 
Reiny,
Yes, your second equation is correct