Question

Apex Grocery wants to build a warehouse that is exactly five miles from each of the routes between stores L, M, and N. Which construction correctly finds the best location of the warehouse?

Answer 1

Answer: Option C - Construction Y because point E is the circumcentre of triangle LMN.

Point E is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.

Step-by-step explanation:

Before solving an algebra problem, it sometimes helps to get a geometric picture of what's happening. Geometry says that three points determine a circle - in other words, given three points that are not

all on the same line, there is exactly one circle which passes through all 3. Finding the point equidistant from the 3 points is the same thing as finding the center of the circle that passes through all of them (since all points on a circle are equidistant from the center).

Our points are L, M and N. Draw the lines LM, LN and MN to form a triangle. Now construct the perpendicular bisectors of any two of the lines, and their intersection, point E, will be the center of this circle.

As shown in the Construction Y because E is the circumcentre of triangle LMN.

This is the best location for the warehouse as it is exactly equidistant from the three stores at L, M and N.

QED!