# 2007 ToT Spring Seniors A1: Coordinate Bashing

##### Solution:

Start out by graphing , and labeling lines and , such that all points are on the line . We label the point , the point , the point , and the point . The lines intersect at the y-axis, which we label to be point .

We start by finding the equation is on. We put the line into the slope-intercept form , where is the slope and is the y-intercept* . Since the line intersects the at the point , we know the y-intercept is . The slope of the line is . Therefore we have . Substituting the point into the equation gives us .
We could also substitute into the equation to give us as well.

We now find the equation is on. Again, put the line into slope-intercept form , where is slope, and is y-intercept*. The lines and intersect at the point , therefore the y-intercept of is . The slope of is . Therefore our new equation is . Substituting either points or give or , where both can be simplified two after expanding and subtract in the first equation, and in the second equation to give .

We are now left with the two equations and . Subtracting the two equations results in   *(note: I changed the slope-intercept form from to to avoid any confusion with point ) # Purpose of Blog

Hello everyone, and welcome to my new site.  This site is run with wordpress.

This problem will have three type of entries:

1. Self proposed problems (where you as the reader are encouraged to post solutions), will be labeled in “Proposed Problems”
2. Solution Problems (these problems are usually contest, or fun proposed problems on the AoPS Forums),  will be labeled in “Solutions”.
3. Articles (articles on a topic in mathematics, such as the Quadratic Formula), will be labeled as “Articles”
Happy problem solving!
~Justin