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!!!

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.

I get the gradient part reiny, but how do you use one of the points to get the equation?

The gradient/slope for BD is -2/7

Ah wait i got the equation for BD as

y=-2/7 x + 16/7

is that right?

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

Yes, your second equation is correct

To find the coordinates of the point of intersection of the diagonals AC and BD, you can follow these steps:

1. Find the equation of the line passing through points A and C:
- Use the formula for finding the equation of a line passing through two points: y - y₁ = m(x - x₁)
- Substitute the values of points A and C: (3,3) and (-1,1)
- Calculate the slope (m) of the line: m = (y₂ - y₁) / (x₂ - x₁)
- Substitute the values into the equation: y - 3 = m(x - 3)
- Simplify to obtain the equation of line AC.

2. Find the equation of the line passing through points B and D:
- Use the formula for finding the equation of a line passing through two points: y - y₁ = m(x - x₁)
- Substitute the values of points B and D: (8,0) and (-6,4)
- Calculate the slope (m) of the line: m = (y₂ - y₁) / (x₂ - x₁)
- Substitute the values into the equation: y - 0 = m(x - 8)
- Simplify to obtain the equation of line BD.

3. Set the equations of line AC and BD equal to each other:
- Equate the two equations obtained in step 1 and step 2, and solve for x:
m₁(x - 3) + 3 = m₂(x - 8)
- Substitute the values of the slopes and intercepts into the equation.
- Solve for x.

4. Substitute the value of x in either line equation and solve for y:
- Substitute the value of x obtained in step 3 into either line equation.
- Solve for y.

5. The coordinates of the point of intersection are (x, y):
- Use the x and y values obtained in step 3 and step 4 to find the coordinates of the point of intersection.

Let me know if you'd like me to walk through the calculations for you.