Need help on Easy Grade 10 Geometry question

**LllamaGlama** · March 27th 2008, 09:24 AM

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!

**topsquark** · March 27th 2008, 09:35 AM

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 $(x_1, y_1)$ and $(x_2, y_2)$ is
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

You have two distances to calculate.

-Dan

**LllamaGlama** · March 27th 2008, 10:21 AM

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?

**topher0805** · March 27th 2008, 10:36 AM

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.

**LllamaGlama** · March 27th 2008, 10:39 AM

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?

**topher0805** · March 27th 2008, 10:43 AM

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?

**LllamaGlama** · March 27th 2008, 10:46 AM

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?

**topher0805** · March 27th 2008, 10:47 AM

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?

**LllamaGlama** · March 27th 2008, 10:50 AM

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

**LllamaGlama** · March 27th 2008, 10:59 AM

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

**LllamaGlama** · March 27th 2008, 11:17 AM

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

Triangle 2: $\sin {b} = \frac {x}{d_2}$ , where $d_2$ 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?

**topher0805** · March 27th 2008, 11:20 AM

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:

$y = mx + b$

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.

**topher0805** · March 27th 2008, 11:26 AM

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

Then add that to the other distance and you have your answer!

**LllamaGlama** · March 27th 2008, 11:29 AM

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:

$y = mx + b$

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.

**LllamaGlama** · March 27th 2008, 11:32 AM

Originally Posted by topher0805

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

Then add that to the other distance and you have your answer!

Huh... i thought i was gonna find the distance from the offshre connecting to the onshore then add the distance from the refinery to the harbour?
that may of been what u just said cuz idk wat a pythagoras is (is that (x2-x2)2+ (y2-y1)2 square rooted?

lol my math typing skills are pretty bad

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