1. ## Need help on Easy Grade 10 Geometry question

A pipleline must be laid to form a straight line along the shore joining the refinery (150,305) to the harbour at (215,-20). A second pipeline is to be laid underwater from an offshore drilling platform located at (210,57) to the first pipeline, at the closest point on the shore. The scale of the grid used for locating the poiints above is in kilometers.
Calculate the distance the oil will flow from the offshore platform to the refinery.

I would really appreciate it if someone can help me on this. The one thing i need to know if how to find the distance to the offshore platform. Thanks alot!

2. Originally Posted by LllamaGlama
A pipleline must be laid to form a straight line along the shore joining the refinery (150,305) to the harbour at (215,-20). A second pipeline is to be laid underwater from an offshore drilling platform located at (210,57) to the first pipeline, at the closest point on the shore. The scale of the grid used for locating the poiints above is in kilometers.
Calculate the distance the oil will flow from the offshore platform to the refinery.

I would really appreciate it if someone can help me on this. The one thing i need to know if how to find the distance to the offshore platform. Thanks alot!
The distance between two points $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ is
$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

You have two distances to calculate.

-Dan

3. The only problem is i only have 1 point for the "offshore drilling platform" my teacher says i need the altitude? I dont have the point that it connects to the line. Do u know how to find that?

4. Originally Posted by LllamaGlama
The only problem is i only have 1 point for the "offshore drilling platform" my teacher says i need the altitude? I dont have the point that it connects to the line. Do u know how to find that?
Altitude? If it's a drilling platform it is at sea level. The altitude is 0.

If you mean the distance from the platform to sea level, it's impossible to find with the information given.

5. Originally Posted by topher0805
Altitude? If it's a drilling platform it is at sea level. The altitude is 0.

If you mean the distance from the platform to sea level, it's impossible to find with the information given.
lol is there no other meanings of altitude? The height of a triangle or something? I thought u needed to find altitudes to get the circumcenter or orthocenrer or somethign like that... must of been mistaken.

How would i find the distance the the on shore pipe to the off shore pipe?

6. Originally Posted by LllamaGlama
lol is there no other meanings of altitude? The height of a triangle or something? I thought u needed to find altitudes to get the circumcenter or orthocenrer or somethign like that... must of been mistaken.

How would i find the distance the the on shore pipe to the off shore pipe?
To find the total distance, simply add these two distance together:

Distance from off shore platform to the harbor + Distance from harbor to refinery.

Use the equation topsquark provided to find these individual distances, noting that the positions given for each location are of the form (x,y).

::Edit:: Ok, I reread the question and I see the problem now. The pipe from the offshore platform is not joining the onshore pipe at the harbor, but rather at the closest point along the shoreline, as both the harbor and the refinery are along the shore.

Well, the shortest distance from the offshore platform will be the line that forms a right angle when it meets the onshore pipeline. Do you know how to find that?

7. Originally Posted by topher0805
To find the total distance, simply add these two distance together:

Distance from off shore platform to the harbor + Distance from harbor to refinery.

Use the equation topsquark provided to find these individual distances, noting that the positions given for each location are of the form (x,y).
Ya i understand that but to find the distance to the offshore i need 2 points which i dont have. Unless i just look at the points i plotted on the graph i have no idea what the point is that connects to the mainland. And if i just used the graph i would fail, which wouldnt be good in the position im in now academicly.

Do u know what i mean how i need a new point?

8. Ok, I reread the question and I see the problem now. The pipe from the offshore platform is not joining the onshore pipe at the harbor, but rather at the closest point along the shoreline, as both the harbor and the refinery are along the shore.

Well, the shortest distance from the offshore platform will be the line that forms a right angle when it meets the onshore pipeline. Do you know how to find that?

9. Originally Posted by topher0805
Ok, I reread the question and I see the problem now. The pipe from the offshore platform is not joining the onshore pipe at the harbor, but rather at the closest point along the shoreline, as both the harbor and the refinery are along the shore.

Well, the shortest distance from the offshore platform will be the line that forms a right angle when it meets the onshore pipeline. Do you know how to find that?
I am very happy u understand it, and sorry i didnt explain it well enough... no i dont know how to find that, thats why i posted cuz i am clueless on that part. If you could explain it that would be great

10. The offshore point doesnt look like a right angle if that is what u mean....

11. Originally Posted by topher0805
Ok, well first find the distances between the offshore platform and both of the other two stations.

Then, use that information and the fact that you know the line that connects the two pipelines will form an angle of 90 degrees.

Notice that the two triangles formed when you draw the line to the onshore pipeline have a common side. Let's call this side x.

So, let's find an equation for this side using both triangles:

Triangle 1: $\displaystyle \sin {a} = \frac {x}{d_1}$ , where $\displaystyle d_1$ is the distance from the offshore platform to the refinery.

Triangle 2: $\displaystyle \sin {b} = \frac {x}{d_2}$ , where $\displaystyle d_2$ is the distance from the offshore platform to the harbor.

Have you calculated the two distances yet?
So do i have to find Dab Dac and Dbc?

12. Hmm, that method doesn't seem to work here.

Ok, here's a simpler way of doing it:

Notice that if the lines connect at a right angle, their slopes will be perpendicular. So, solve for the slope of the line connecting the refinery and the harbor. Once you have the slope, recall that if a slope is perpendicular that means it's slope is the negative reciprocal.

So, take the negative reciprocal of the slope that you find. Then, use the point on the line that you already have (210,57) to find the equation for that line in the form:

$\displaystyle y = mx + b$

Then, find the equation of the line joining the refinery and the harbor.

Set the two equations equal to each other to find the x coordinate at which they meet, and then plug that into either equation to find the y coordinate.

Then, use your now point in combination with your previous point of (210,57) to find the distance between them.

13. Oh, and you need the distance from where they connect to the refinery, so just Pythagoras for that.

14. Originally Posted by topher0805
Hmm, that method doesn't seem to work here.

Ok, here's a simpler way of doing it:

Notice that if the lines connect at a right angle, their slopes will be perpendicular. So, solve for the slope of the line connecting the refinery and the harbor. Once you have the slope, recall that if a slope is perpendicular that means it's slope is the negative reciprocal.

So, take the negative reciprocal of the slope that you find. Then, use the point on the line that you already have (210,57) to find the equation for that line in the form:

$\displaystyle y = mx + b$

Then, find the equation of the line joining the refinery and the harbor.

Set the two equations equal to each other to find the x coordinate at which they meet, and then plug that into either equation to find the y coordinate.

Then, use your now point in combination with your previous point of (210,57) to find the distance between them.
K im trying to do the calculations now. If i hit a road block (which i can almost gaurentee i will) ill post again. Thanks for the help this is an amazing site.

15. Originally Posted by topher0805
Oh, and you need the distance from where they connect to the refinery, so just Pythagoras for that.