Question

Three schools are located at points A, B, and C. The school district wants to locate its new stadium at a location that will be roughly the same distance from all 3 schools. Where should they build the stadium? Explain or show your reasoning.​

Answer 1

I have attached the image showing the location of the three schools.

Answer:

Should be built at the centroid of the triangle formed by points A, B and C.

Explanation:

From the attached image, we see that if we join the 3 points by a straight line, they will form a triangle.

Now, to get a location that will be roughly the same distance from all 3 schools, it means a point that is equal to each of 3 vertex of the triangle.

The point that is equal to each vertex of a triangle is known as "Centroid".

Now, to find this centroid, we will add up the (x, y) coordinates of the 3 vertex and divide by 3.

For example;let's assume ;A has a coordinate of (x1, y1) ; B has a coordinate of (x2, y2) ; C has a coordinate of (x3, y3).

The coordinates of the centroid will be;

[(x1 + x2 + x3)/3], [(y1 + y2 + y3)/3]