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

Explanation:

Step1: Recall the properties of equidistant points

The point equidistant from the vertices of a triangle is the circum - center (center of the circum - circle), and the point equidistant from the sides of a triangle is the in - center (center of the in - circle).

Step2: Analyze Construction X

In Construction X, there is an in - circle (a circle tangent to the sides of the triangle). The center of the in - circle (point \(C\)) is equidistant from the sides of \(\triangle LMN\), not from the vertices \(L\), \(M\), and \(N\).

Step3: Analyze Construction Y

In Construction Y, there is a circum - circle (a circle passing through the vertices of the triangle). The perpendicular bisectors of the sides of a triangle intersect at the circum - center. The circum - center is equidistant from the vertices of the triangle.

Answer:

Construction Y.