On the back of the map was written:
Start halfway between the rock and the old stump. Walk so that the distance between ye and the stump is always the same as the distance between ye and the rock. When ye be exactly northwest of the waterfall, ye be standing on my buried treasure.
Using her algebra skills, Callie was able to determine exactly where Algebeard's loot was stashed. What are the coordinates where Callie should dig? There are a variety of ways to solve this problem.
S.R.
ReplyDelete(20,8)
I graphed the points found the middle of the line that connected the rock and the slump and moved it so it has northwest of the waterfall
MNH
ReplyDelete(20,8)
I graphed the points, and found the middle of the line that connected the rock and the slump and moved it so it was northwest of the waterfall.
A.C.M.
ReplyDeleteThe buried treasure is located at (21,7) on the graph. I solved this by first finding the midpoint. You can solve that by having the equation/coordinate points, (X1+X2)/2, (Y1+Y2)/2. I plugged in the x and y’s of the stump and rock’s coordinate points. The midpoint was (7,3). Then, I went down the graph to the east until I was exactly NW of the waterfall, which was the point (21,7).
MJH
ReplyDeleteThe midpoint between the stump and the rock is (3,7)
The slope of that line is -2
If you must always be evenly apart between the stump and the rock, then you must find the line that is perpendicular, and the slope of that line is ½
If the treasure is exactly northwest of the waterfall, then it is buried at the point (15,13)
J.H.
ReplyDeleteWhen you find the midpoint you would do y1+y2/2. In this problem you would find the midpoint between the rock and the stump. You would use the equation y1+y2/2, y1+y2/2. Using the equation, with the stump and the rocks points you would get (3,7) The clues from the map say that the buried treasure would be the midpoint northwest of the rock and the stump. When you would graph out the points, you would get a 45 degree angle from the waterfall to the northeast, the waterfall is west from the midpoint. The lines intersect at the point (21,7) where the treasure is located.
A.A.M.
ReplyDeleteYou can find the midpoint between the stump and the rock by using the equation
(x1+x2 , y1+y2). The results of that equation
2 2
between the stump and the rock for the
coordinate points would be (3,7). The clues from the back of the map say that the treasure is exactly northwest of the midpoint of the rock and stump. If you draw a straight line from the mid point to the right and then draw a 45 degree angle from the waterfall to the northeast (because the waterfall is to the west of the midpoint) the lines intersect at the point (21,7) where pirate Algebeard buried his treasure.
E.D.
ReplyDeleteI used a graph to plot the coordinate points of the stump, the rock, and the waterfall.
Once I had the stump and the rock plotted, I drew a straight line connecting the points. The slope was -8/4, or -2/1, or -2. Halfway between the two points was (3,7).
I then found (3,7) and drew a line accross the graph, making it clear where that line was on the graph. Then, using the slope and the waterfall coordinates, I found that the treasure would (i'm pretty sure) be buried at the coordinate points (22,7)
:)
JB The midpoint between the rock and the stump is (3,7).The slope is -2. If you must be always the same distance from the rock then you have to find the perpendicular line. The northwest perpendicular line points would be (15,13).
ReplyDeleteO.S
ReplyDeleteSince I graphed my results,I used intervals of five. Also, since the treasure map says to go exactly north west of the falls,in the amount of distance between the stump, the coordinates would be (15,15), and the slope is 3.
S.G.
ReplyDeleteI graphed the coordinates, and found the slope between the stump and the rock. The slope is -2. I found the coordinate point between the line, and got (3,7). I drew a line northwest from the waterfall, then drew a line coming from the coordinate point (3,7), and whatever point it intersected with, that is where the treasure is buried. The coordinate point is (21,7), which I believe where the treasure is buried.
N.H.
ReplyDeleteBy following the provided directions, the midway point between the rock and stump is (3, 7). By following the path until exactly northwest of the water fall you get the points (22, 14).
M.W.
ReplyDeleteIn order to solve this problem, I first made a graph on graph paper and plotted the points given on the picture, (1,11), (5,3), and (26,2). I found halfway in between and to was about 6 on the y axis of the graph. Then it said to stop when Callie gets exactly northwest. So I drew a line about Northwest from the water fall. Then, I continued to draw a line from 6 on the y axis, halfway between the rock and the stump, until I met the line I made that was northwest of the water fall. I then found the coordinate points of the spot where my two lines met. That coordinate point was, (6,22).
The coordinate point of the spot where Callie should dig is (6, 22)
N.H.
ReplyDeleteBy following the provided directions, the midway point between the rock and stump is (3, 7). By following the path until exactly northwest of the water fall you get the points (16, 12).
P.M.
ReplyDeleteThe midway point of the rock and stump is (3,7). If you follow the diresctions using a graph, I get (16, 12)
M.D.
ReplyDeleteCallie was vacationing in the Caribbean when she found a treasure map made by the famous pirate Algebeard many years before:
On the back of the map was written:
Start halfway between the rock and the old stump. Walk so that the distance between ye and the stump is always the same as the distance between ye and the rock. When ye be exactly northwest of the waterfall, ye be standing on my buried treasure.
Using her algebra skills, Callie was able to determine exactly where Algebeard's loot was stashed. What are the coordinates where Callie should dig? There are a variety of ways to solve this problem.\
To start off solving this equation, I first plotted the points of all the significant landmarks (the rock, old stump, and waterfall.) I found the slope between the points of the rock and old stump, which was 8/4, or 2. Then I knew that you must start halfway between the rock and old stump, so I found the point that met up 4 and over 2 from the rock. The point where you must start finding the treasure, I found, was (3,7). I then went to the opposite end of the problem to figure out exactly where Northwest of the waterfall would be. I decided to make the line parallel to the x-axis North and the one going up on the y-axis West, since Northwest is right between North and West. So what I did was draw a straight lines starting at the point for the waterfall going straight and being parallel with the x-axis, and another line starting at the point for the waterfall and going straight up being parallel with the y-axis. I knew that to make it exactly Northwest, the slope going up from the line I just drew would be 1/1, or 1. When I plotted the points using that slope and starting at the point for the waterfall, I got points making a line going exactly Northwest from the waterfall.
Now that I had a frame of reference from where Northwest of the waterfall might be, I went back to my point that was between the rock and old stump.
Next, I knew that it would be hard to move staying the exact same distance from each. I drew a line going out from the point of the rock, and a rock going out from the stump’s point. I stayed at the same slope from the rock, moving up one and over one everytime, and eventually I met up with the line going Northwest from the waterfall. The treasure was located at (12,16).
B.H.
ReplyDeleteIn this problem, we had to find a certain point on a map that is set up on a coordinate grid. This point has to be exactly North West of one point (26, 2) the waterfall. Also, the point must fall exactly between two other points (5, 3) the rock and (1, 11) the stump. Draw a ray that runs directly North West of the waterfall. If I plot the point (3, 7), this point falls exactly between the stump and the rock, but does not fall exactly North West of the waterfall. If I plot point (7, 9) it also falls between the rock and stump, but is not North West of the waterfall; point (11, 11) is also like this. But then if I plot point (15, 13) this point falls between the stump and the rock and is exactly North West of the waterfall. The treasure is located at (15, 13).
What I did to find the answer was I graphed out what the problem told me. Then I found the middle between the stump and the rock which was (3,7). Then I graphed the waterfall on my graph. I found which direction northwest was. I then used a straight edge to keep a straight line between each of the points. I think that Callie should start digging to find the treasure at (20,15.
ReplyDelete-RW
The coordinate point that Callie should start digging at is (20,15). The first thing that I did was find the midpoint between the rock and the stump. The point is (3,7). Heading northwest, while remaining the same walking distance between the two points. It was decided to stop at (20,15) which lies northeast of the waterfall. TM
ReplyDeletewhat i did was plot the points that the map showed me then i used a straight edge up against another straight edge to find points that would be the same distance apart from the stump and rock. then drew a line till it was northwest of the water fall to get my point. then came to the point (20,15)D.E.
ReplyDeleteS.S.
ReplyDeleteWhen solving this problem, the first thing that I did was graph the coordinates that I had. After graphing the coordinates, I started to read the first part of the question. “Start halfway between the rock and the old stump.” Half way between the stump would be X equals 3. The next part of the question went on by saying, “Walk so that the distance between ye and the stump is always the same as the distance between ye and the rock.” With all of that information, I decided that a good coordinate to start at would be (3, 7) because that follows both guide lines. Since the next part of the question had to do with direction, to help myself out, I decided to make sure of all of the directions just to be on the safe side. As the last part said, “When ye be exactly northwest of the waterfall, ye be standing on my buried treasure.” Key word northwest, the next thing I did was go over to the coordinates of the waterfall. To be northwest of the waterfall, that meant that it had to go back 1 (to the left) and move up one. This ended me up with the coordinates (25,3) which are northwest of the waterfall. With all of this information I was able to get to the coordinate points where Callie should dig up which shall be (25,3) .
New answer, sorry. Its (21,7)
ReplyDelete-RW
New answer. Callie should start at (21,7) TM
ReplyDelete(21,7)
ReplyDeleteBC
New answer. Again. Sorry. She shouls start digging at (19,9) TM
ReplyDeleteI think the answer is (19,9)
ReplyDeleteMG
Sorry again, new answer.
ReplyDeleteIts (19,9)
^ Thats the point she should start digging.
Sorry, again. Haha.
-RW
Just kidding. (19,9)
ReplyDeleteBC
JHS
ReplyDeletePOW THURSDAY, OCTOBER 28, 2010
I found the halfway point between the stump and the rock by using the equation we learned in AL. The equation is: AB= the square root of, (X2-X1) squared + (Y2-Y1) squared. The mid-way point was (3,7)
Next I guessed that the mid-point between the stump and the waterfall would be exactly “northwest” I used the same equation to get the coordinates of, (13,7) this was on the same Y axis of (3,7) so I know this is where the “treasure” was buried.
CA
ReplyDeleteThe points where the treasure is are (21,7). First, I plugged all the points for the stump, rock, and waterfall onto a graph. Then I connected the stump and the rock and made a triangle, just like you would do if you were going to use rise over run to find the slope. The rise was 8, so I divided that in half and got 4, since you have to walk exactly between the stump and the rock. Then I found the waterfall on the graph and made a line that went over every point northwest of it. I drew my line from between the stump and the rock and kept going until I reached the line I drew for the waterfall and they intersected at the points (21,7).
M.N
ReplyDeleteThe treasure is buried exactly northwest of the waterfall. The coordinate points are 16,9 because you have to walk the same distance and stop exactly northwest of the waterfall. So I make sure that my coordinate points are going at a constant rate so that it will always be between the stump and rock. The coordinate points 16,9 were the closest thing to northwest because past that point it isn’t northwest.
M.O.
ReplyDeleteFirst, I made a graph and plotted the points from the map onto it. I found the slope of the distance between the rock and the stump to make sure that I would have the exact coordinate point for that. I followed along the x-axis until I seemed really close to being NW of the waterfall. My coordinate points in the end are (24,7).
JS and SA
ReplyDeleteThe point of the treasure is (11, 11)
Solution one-First we started out between the rock and the stump, (3, 7)
After we did that we thought walking in a straight line would keep us evenly between the rock and the stump, but sadly it did not. We then sat back and tried taking various approaches at this problem. We were confused when the problem said exactly northwest. We tried finding many points that were evenly spaced between the stump and the rock, and was also northwest. After that we discovered that would never happen and started trying to find paths the person could take to stay exactly between the rock and the stump. We then decided to find the end point or where he finished by using the distance formula to see how far away from the rock and how far away from the stump he was. We plugged in many point then adjusted if is was to close to one object. We finally tried (11, 11) and it was the same distance apart from both the rock and the stump. It was also northwest of the waterfall so we knew we found our X.
Solution two- Now we made a square using the points of the stump and rock; the four points of the square are A(1,11), B(5,3), C(13,7), and D(9,15). After we did this, we found the midpoint of line CD which had the coordinates of (11, 11). We found this by using the midpoint equation. After finding this, we measured the distance of it from the stump (1, 11) and the rock (5, 3). The distances were the same, 10 units. It also was northwest of the waterfall. So, now we knew where X was located and we could get treasure.
S.S.
ReplyDeleteWhen solving this problem, the first thing that I did was graph the coordinates that I had. After graphing the coordinates, I started to read the first part of the question. “Start halfway between the rock and the old stump.” Half way between the stump would be X equals 3. The next part of the question went on by saying, “Walk so that the distance between ye and the stump is always the same as the distance between ye and the rock.” With all of that information, I decided that a good coordinate to start at would be (3, 7) because that follows both guide lines. Since the next part of the question had to do with direction, to help myself out, I decided to make sure of all of the directions just to be on the safe side. As the last part said, “When ye be exactly northwest of the waterfall, ye be standing on my buried treasure.” Key word northwest, the next thing I did was go over to the coordinates of the waterfall. To be northwest of the waterfall, that meant that it had to go back 1 (to the left) and move up one. This ended me up with the coordinates (25,3) which are northwest of the waterfall. With all of this information I was able to get to the coordinate points where Callie should dig up which shall be (25,3) .
SD
ReplyDeleteMidpoint 3, 7
Slope:-2x, opposite y= ½ x
Northwest: y= -x
Using this I found how high (y) on the map I should be (13) and how far (x) I would have to go with the slope of ½ to get to that (15).
This could be done using a picture,
or solving(3+x)+(7+½ x)=(2-x)+(26-x), taking that answer and substituting x in y= ½ x from the coordinate 3, 7.
(21,7) SM.
ReplyDeletethe answer i got was 12,16 as the coordinate point that the buried treasure is at. i did this by drawing a line that goes northwest of the waterfall then drew a line that kept the stump and rock the same distance apart. Where they met is the point i used.
ReplyDeleteGrant Watts
ReplyDeletePeriod 7
I got my conclusion by making a graph and plotting the points and staying in the middle of the rock and the tree stump. Callie should dig on the point 19, 9. X=19 Y=9. I got this because I got the run and the rise and the middle way point.
H.H. and J.D.
ReplyDeleteI first drew a diagonal line going Northwest. Then I found the midpoint of the rock and the stump. Then since it says you have to stay the same length away I just created an isosceles triangle and went up to the northwest line.