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.

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

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

Step-by-step 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]

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.

(6,0) i hope it makes enough sense