To determine the best location for the warehouse that is equidistant from stores L, M, and N, we need to identify the circumcenter of the triangle formed by these three points. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect, and it is equidistant from all three vertices (stores in this case).
Let’s go through the steps to solve this problem:
1. Identify the Construction Steps:
- We need to construct the perpendicular bisectors of all three sides of the triangle formed by points L, M, and N.
- The point where these perpendicular bisectors intersect will be the circumcenter (equidistant from all three points).
2. Examine the Options Provided:
- Construction X: Look for the construction steps in Construction X to determine if it involves perpendicular bisectors intersecting at a point, which would be the circumcenter.
- Construction Y: Similarly, look for the steps in Construction Y to determine if it involves perpendicular bisectors intersecting at a point, which would be the circumcenter.
3. Determine the Correct Construction:
- Construction X has a point C (we need to verify if C is the circumcenter by checking for perpendicular bisectors).
- Construction Y has a point E (similarly, check if E is the circumcenter by checking for perpendicular bisectors).
4. Decide Based on the Intersection of Perpendicular Bisectors:
- If in Construction Y, point E is where the perpendicular bisectors of the triangle's sides intersect, then E is the circumcenter.
- If in Construction X, point C is where the perpendicular bisectors of the triangle’s sides intersect, then C is the circumcenter.
Based on the steps mentioned, we conclude:
Correct Answer: Construction Y, because point E is the circumcenter of triangle LMN.
So, the construction that correctly finds the best location of the warehouse, which is equidistant from the three stores L, M, and N, is Construction Y where point E is the circumcenter of the triangle LMN.
