Perhaps you've heard of the famous English pirate named Blackbeard, but did you ever hear about his Spanish cousing, Barbanegra? Probably not. He was the mathematician of the high seas. When he buried his treasure, he did so in a very algebraic manner. Really!

For example, once after a very successful raid on a rich merchant ship, he took three of his most trusted henchmen onto the island with the loot to bury it in a very special way. Barbanegra stood by a certain palm tree with a long string in his hand, Holding one end in his hand, he gave the other end to one of his men and directed him to walk 6 varas straight south, then 8 varas due east.

He gave another string to each of the other two men, instructing one to walk a spot 6 varas due east and 2 varas due north of the tree. He told the third man to walk to a spot that was 6 varas due south and 2 varas due west.


Once everyone was in position, the strings were stretched taut, forming two straight lines. The spot where they crossed was the place that Barbanegra wanted to dig a hole to store his treasure. And they did just that.

Your task now is to determine the coordinates of that "X" spot, given that coordinate pair for the tree is (3, 4).

No, it's not our task, it's yours ;)

Start from (3, 4), where will be the next point?

1. "directed him to walk 6 varas straight south, then 8 varas due east. "

Then, the next point;

2. "instructing one to walk a spot 6 varas due east and 2 varas due north of the tree"

and a last point;

3. "He told the third man to walk to a spot that was 6 varas due south and 2 varas due west."

Can you deduce the 3 points, and use them to find the equations of the two lines which pass through those points? Making a sketch is very handy.

Then use simultaneous equations to get the point of intersection of those lines.

Post what you get! :)

Okay, so I drew the lines and the slope of 3,4 and 11, -2 is 3/4 and the slope of 9,6 and 1, -2 is 1. I don't know what to do from here, though.

Slight correction, the gradient for the first two points is -3/4.

Okay, you need to get the equation of those two lines now.

I know two methods. Maybe you know the y = mx + c method.

m is the gradient, and you pick a point (x, y) on the line. (for example (3, 4) ).

(4) = (-3/4)(3) + c

c = 25/4

So, the equation of the first line is y = (-3/4)x + 25/4

You do the same with the other line now.

Thanks for the help. Using your info, I solved the rest and got the answer: 5 2/7 and 2 2/7.
Thanks a bunch!

Well done! :)