Question

from unit 1, lesson 9 three schools are located at points a, b, and c, which are represented in the following diagram. the school district wants to build its new stadium at a location that will be roughly the same distance from all three schools. where should they build the stadium? explain or show your reasoning.

Explanation:

Step1: Recall geometric concept

The point that is equidistant from three non - collinear points is the circum - center of the triangle formed by those three points.

Step2: Construct perpendicular bisectors

Construct the perpendicular bisectors of the line segments connecting points A, B, and C (i.e., AB, BC, and AC). The perpendicular bisector of a line segment is the set of all points that are equidistant from the two endpoints of the line segment.

Step3: Find the intersection point

The point where these three perpendicular bisectors intersect is the circum - center of the triangle ABC. This is the location where the stadium should be built as it will be roughly the same distance from all three schools A, B, and C.

Answer:

The stadium should be built at the circum - center of the triangle formed by points A, B, and C, which is the intersection point of the perpendicular bisectors of line segments AB, BC, and AC.