# Point of Concrrency Project

### By Sarah Wales

## Scenario

The Martins just bought a new house and want to put in a wooden patio in the shape of a triangle. The patio will extend along the exterior wall of the bedroom and connect at a right angle with the wall of the living room. The points of each corner of the walls are (0,0), (16,12), and (4,28). There will be a tree placed inside the triangle to provide shade for the patio and it is equal distance from each vertex. Find the location where the tree should be placed using a point of concurrency.

## Steps

1. Use the midpoint formula to find the midpoint of each segment of the triangle.

2. Connect each midpoint to its opposing vertex creating an intersection point where the tree will be placed.

3. Now find the slope of the line containing a vertex and midpoint that was created in step two.

4. Find the equation in slope intercept form of the line.

5. Complete steps three and four for another line containing a midpoint and vertex.

6. Set both equations equal to each other and solve for x.

7. Then, plug in the value for x into one of the equations and solve for y.

8. The x value is the x-axis and the y value is the y-axis creating the point of intersection, known as the point of concurrency.

## Explanation

The point of concurrency that best fits this scenario is a centroid representing the tree that will placed inside the Smith's patio. To find this point of concurrency the medians are needed to be found to create a point of intersection that represents the tree.