Question

Apply A farmer wants to place a hay bale so that it is

the same distance from Gates L, M, and N. Construct
the location P where he should place it.
L
N
M

Answer 1

Placing the hay bale at the circumcenter ensures that it is the same distance from all three gates, L, M, and N. This is because the circumcenter is equidistant from all the vertices of the triangle.

The farmer should place the hay bale at the circumcenter of the triangle formed by Gates L, M, and N. The circumcenter is the point where the perpendicular bisectors of the triangle's sides intersect.

Here's how to find the location of the circumcenter:

1. Draw the perpendicular bisectors:

- For each side of the triangle, draw a line that passes through the midpoint of the side and is perpendicular to it.

2. Find the intersection point of the perpendicular bisectors:

- The point where the three perpendicular bisectors intersect is the circumcenter.

In the image the circumcenter is already marked as point P. Therefore, the farmer should place the hay bale at point P.

Placing the hay bale at the circumcenter ensures that it is the same distance from all three gates, L, M, and N. This is because the circumcenter is equidistant from all the vertices of the triangle.

Answer 2

To place the hay bale equidistant from Gates L, M, and N, find the circumcenter of the triangle formed by these points, which is where the perpendicular bisectors of the triangle's sides intersect.

Step-by-step explanation:

The question is asking to construct the location P where a farmer should place a hay bale such that it is equidistant from three gates, named L, M, and N. This is a classical construction problem that can be solved using the concept of the circumcenter of a triangle, which is the point where the perpendicular bisectors of the sides of the triangle intersect. The hay bale should be placed at the circumcenter of the triangle formed by Gates L, M, and N to ensure that it is the same distance from all three gates.

To construct the circumcenter:

1. Draw the triangle with vertices at L, M, and N.
2. Construct the perpendicular bisector of at least two sides of the triangle. This can be done by finding the midpoint of a side and drawing a line at a right angle to it.
3. The point where these bisectors intersect is the circumcenter P.

Place the hay bale at the circumcenter P to ensure it is equidistant from all three gates.