Posted by **Sal** on Wednesday, January 30, 2013 at 7:51pm.

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**, Wednesday, January 30, 2013 at 8:24pm
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

**x - 2y = -3**

Now you find the equation for BD

then solve the two equations.

- Geometry -
**Sal**, Wednesday, January 30, 2013 at 8:31pm
I get the gradient part reiny, but how do you use one of the points to get the equation?

- Geometry -
**Sal**, Wednesday, January 30, 2013 at 8:32pm
The gradient/slope for BD is -2/7

- Geometry -
**Sal**, Wednesday, January 30, 2013 at 8:35pm
Ah wait i got the equation for BD as

y=-2/7 x + 16/7

is that right?

- Geometry -
**Reiny**, Wednesday, January 30, 2013 at 8:37pm
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

- Geometry -
**Reiny**, Wednesday, January 30, 2013 at 8:41pm
Yes, your second equation is correct

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