1. ## Basic Coordinate Geometry -Help Please!

Hello all,

It's been many years since I attempted a problem of this kind (apparently, a basic coordinate geometry question). Your help would be much appreciated.

So here it is,

"Let us assume that we have a line from coordinates E1, N1 to E2, N2. What we want to know is where this line will intersect a particular line that runs from North to South."

"If we know the coordinates of the two points and the Easting value of the line, how do we calculate the coordinates at which the projected line between the two points crosses the N-S line.?"

*I can find the midpoint of two lines, and the distance between, but not the very point at which they intersect. I'm trying to do this on an Excel Spreadsheet by the way! (also new to me)

E1 2607.05 N1 3518.08 E2 3746.93 N2 3734.63These coordinates make up one Line. The easting value of the line is 4000.

All other given info is as follows:

"Label cells A9 and A10 with DeltaE and DeltaN respectively and enter in formulae to calculate these values in cells B9 and B10 (Hint: remember that a delta value represents a difference in values, so DeltaE will be the difference between E1 and E2)." Therefore, DeltaE=1139.88, and DeltaN=216.55

"Label C9 Bearing(rad) and C10 Bearing(degs). In D9 enter the formula =ATAN(B9/B10) and in D10 enter =Degrees(D9)"

"Devise a formula to enter into cell D5 so that the northing of the point where the extended line between the two points crosses the 4000 East edge."

Sorry to draw this out so much, but I've at least included every detail!

Basically, I need a formula to find the intersection of two lines.

Thanks again

2. Originally Posted by BaxterN
Hello all,

It's been many years since I attempted a problem of this kind (apparently, a basic coordinate geometry question). Your help would be much appreciated.

So here it is,

"Let us assume that we have a line from coordinates E1, N1 to E2, N2. What we want to know is where this line will intersect a particular line that runs from North to South."

"If we know the coordinates of the two points and the Easting value of the line, how do we calculate the coordinates at which the projected line between the two points crosses the N-S line.?"

*I can find the midpoint of two lines, and the distance between, but not the very point at which they intersect. I'm trying to do this on an Excel Spreadsheet by the way! (also new to me)

E1 2607.05 N1 3518.08 E2 3746.93 N2 3734.63These coordinates make up one Line. The easting value of the line is 4000.

All other given info is as follows:

"Label cells A9 and A10 with DeltaE and DeltaN respectively and enter in formulae to calculate these values in cells B9 and B10 (Hint: remember that a delta value represents a difference in values, so DeltaE will be the difference between E1 and E2)." Therefore, DeltaE=1139.88, and DeltaN=216.55

"Label C9 Bearing(rad) and C10 Bearing(degs). In D9 enter the formula =ATAN(B9/B10) and in D10 enter =Degrees(D9)"

"Devise a formula to enter into cell D5 so that the northing of the point where the extended line between the two points crosses the 4000 East edge."

Sorry to draw this out so much, but I've at least included every detail!

Basically, I need a formula to find the intersection of two lines.

Thanks again
This is just going to look NASTY!

Given two points (x1, y1) and (x2, y2) one formula for the line connecting the two will be:
y = [(y2 - y1)/(x2 - x1)]x + [y2 - (y2 - y1)*x2/(x2 - x1)]

So given two pairs of points (x1, y1); (x2, y2) and (x3, y3); (x4, y4) we have to solve the set of simultaneous equations:
y = [(y2 - y1)/(x2 - x1)]x + [y2 - (y2 - y1)*x2/(x2 - x1)]
y = [(y4 - y3)/(x4 - x3)]x + [y4 - (y4 - y3)*x3/(x4 - x3)]

I'm not going to do it without LaTeX: as I said it's going to look ugly. But you can work it out from here.

-Dan

3. Cheers.