1) The Vietnam Memorial in Washington, DC is an angular wall. If you are standing at the vertex of the angled monument and you wish to back up always staying equidistant from the side walls, describe the path you would take.
2) Describe fully the locus of points 6 units from the origin. Write an equation of the locus.
1) The Vietnam Memorial in Washington, DC is an angular wall. If you are standing at the vertex of the angled monument and you wish to back up always staying equidistant from the side walls, describe the path you would take.
2) Describe fully the locus of points 6 units from the origin. Write an equation of the locus.
Uhh I don't know
1) To back up while always staying equidistant from the side walls of the Vietnam Memorial, you would need to follow a circular path around the vertex of the angled monument. This is because the distance from a point on a circle to its center is always the same.
To start, let's assume that the vertex of the monument is located at the origin on a coordinate plane. The side walls can be represented by two lines, each extending from the origin at a different angle. As you back up, you would need to maintain a constant distance from both lines at all times.
To achieve this, imagine drawing two imaginary circles with their centers at the origin. The radius of each circle would be the distance from the vertex to the nearest side wall. As long as you stay on the circumference of both circles, you will always be equidistant from the side walls.
As you back up, your path would form a circular trajectory around the vertex, keeping the same distance from both side walls. The angle at which you circle around the monument would depend on the specific angles of the side walls.
2) The locus of points that are 6 units away from the origin forms a circle centered at the origin. A locus of points is the path traced out by a moving point that satisfies a given condition, in this case, being 6 units away from the origin.
To write an equation for the locus, we can apply the Pythagorean theorem, which states that the square of the distance from the origin to a point (x, y) is equal to the sum of the squares of its coordinates:
x^2 + y^2 = r^2,
where r is the radius of the circle. In this case, since we want points that are 6 units away from the origin, the equation becomes:
x^2 + y^2 = 6^2,
or
x^2 + y^2 = 36.
This equation represents the locus of points that are 6 units away from the origin, forming a circle with a radius of 6 units.