Answer: By calculating the centroid, Kai can determine the point where the triangular paper airplane needs to be positioned on the pencil to achieve balance.
Explanation:
In order for the triangular paper airplane to balance on a pencil, Kai would need to calculate the center of mass of the airplane. The center of mass is the point where the weight of an object is evenly distributed.
To find the center of mass of the triangular paper airplane, Kai would need to calculate the centroid of the triangle. The centroid is the point where the medians of the triangle intersect, and it is also the center of mass of the triangle.
Here are the steps Kai can follow to calculate the centroid and determine the point where the airplane needs to balance:
1. Identify the coordinates of the three vertices of the triangle on the coordinate plane printed on the paper airplane. Let's label these vertices A, B, and C.
2. Calculate the average of the x-coordinates of the three vertices. This will give the x-coordinate of the centroid. Similarly, calculate the average of the y-coordinates of the three vertices to find the y-coordinate of the centroid.
3. The coordinates of the centroid will give the point where the airplane needs to balance. Let's label this point as P(x, y).