Point Of Currency Project

By:Michelle Barker

Scenario

Penny is rearranging her bedroom. She put her bed against the right side of her wall, her desk against the left side, and her vanity by the door. She wants to find a way to put her new bean bag equidistant from all three pieces of furniture. If the three pieces of furniture have the points of (3,1), (-2,1), and (1,3), where should Penny place the beanbag?
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Steps

To find a point that is equidistant from each or the points we are going to find the circumcenter!


1. Find the midpoint using the midpoint formula for each line.

2. Find the slope of each line.

3. Find the negative receptacle of each slope to have your slopes for the perpendicular bisectors.

4. Now that we have a slope and an ordered pair of the perpendicular bisectors ( the midpoints), we can find the equation of the lines! Substitute what you already know into slope intercept form and solve for b. You then will have the equation for the line.

5. Now that we have equations for all the perpendicular, we can now find the cimcumcenter of the triangle. Put two of your slope intercept equations in an equation and solve for X.

6.Once you have the value of X, plug that into a slope intercept formula to solve for Y.

7. Once you have found Y, you have an ordered pair! This is your circumcenter.

Conclusion

The points of the circumcenter of the triangle are (5/2,11.5). Finding the circumcenter was the most relevant point of concurrency because Penny wanted to place her bean bag equidistant from each piece of furniture or the vertices of the triangle!