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!!!
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.
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?
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
Answered by Reiny
Yes, your second equation is correct