Callie's Cruise

Callie 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.

October 15th

A Triangle's Area

Each of two congruent triangles has an area of 24 square units. Their vertices are determined by the intersection of the lines with equations:

y = -4
x = 0
y = (-3/4)x + b

Determine the two values of b that will identify the lines needed to form these triangles.
You may want to use some graph paper as you investigate and analyze this problem; however, a drawing is not required in your submission.

Oct 8th

Here is the solution for the problem below.  I was impressed at your thinking and methods in attempting to solve the problem.  Beautiful job!!!!  My only concern is very few or you proceeded to tell me what the "?" numbers were.  Than means that many of you didn't address the actual question asked.  Please read carefully.  ;-)

Suppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b  which is less than 10 and −10 is less than c+d  which is less than −5

Given this information, what can you conclude about these inequalities?