Question

apex grocery wants to build a warehouse that is equidistant from its three stores, l, m, and n. which construction correctly finds the best location of the warehouse? construction x construction y construction y because point e is the in - center of \\(\triangle lmn\\)

Explanation:

Step1: Recall geometric - center properties

The point equidistant from the vertices of a triangle is the circum - center. The circum - center is the intersection of the perpendicular bisectors of the sides of the triangle.

Step2: Analyze Construction X

Construction X shows the intersection of angle bisectors, which gives the in - center. The in - center is equidistant from the sides of the triangle, not the vertices.

Step3: Analyze Construction Y

Construction Y shows the intersection of the perpendicular bisectors of the sides of \(\triangle LMN\). The intersection point \(E\) is the circum - center of \(\triangle LMN\), which is equidistant from the vertices \(L\), \(M\), and \(N\).

Answer:

Construction Y, because the point \(E\) is the circum - center of \(\triangle LMN\) and the circum - center of a triangle is equidistant from its vertices.