Chapter 4.7, Problem 19WE

a.

To determine

To determine the location of the point B .

Explanation of Solution

Given:

Concept used: Properties of triangles.

The given figure,

Now to determine the point B , this is to be located near the lake − front and must be equidistant from the recreation center and the school, the figure will form an isosceles triangle whose two sides are equal in length,

Both the sides are equal in length, say l units,

Conclusion:

Hence, the above figure gives a desired location for the point B .

b.

To determine

To determine the location of the point $L$ .

Explanation of Solution

Given:

Concept used:

Concept of geometry.

The given figure,

Now to locate the point $L$ , that is to be at boat launching site which is equidistant from the Elm Road and the Main Street, the figure will form a square,

Since the sides of a square are always equal, both the distances (that is, the perpendicular distance from the Elm road to the point L , and the perpendicular distance from the Main Street to the point L ) are equal. Therefore, the point L is equidistant from the Elm Road and the Main Street,

In the above figure, both the distances are of $a$ units.

Conclusion:

Hence, the above figure gives a desired location for the point L .

c.

To determine

To determine the location of the point F .

Explanation of Solution

Given:

Concept used: Properties of triangles.

The given figure,

Now to find the location of the point F , that is to be a flag pole which is equidistant from the recreation center, courthouse and school, the point will be in the middle of the two and a straight path to the other as shown below;

Since, it is given that all the distances from the point F to the recreation center, courthouse and the school are equal in length, the recreation center, courthouse and the school are all equidistant from this point.

So, from the properties of similar triangles and since all of the above-mentioned distances are equal, say of $b$ units, both the above triangles must be equilateral.

Conclusion:

Hence, the above figure gives a suitable location for the point F .