Question 3 (Multiple Choice Worth 4 points)
[6.03] If you wanted to eliminate the y variable by adding the two equations in the following system, what could be your first step?
2x − 4y = 6
3x − y = 12
Yes, except when the line is in the plane. In the latter case, they intersect at each point on the line (an infinite number).
If the line is not IN the plane ... it just zaps through the plane from some direction ... then it touches the plane in only one point. The intersection is a point.if it is lined up with the plane, then the intersection is a line.
I believe the answer is "perpendicular line". Forgive me if I'm wrong :)
Yes, that's pretty much the definition of parallel.
Graphing a line on the coordinate plane is the two-dimensional equivalent to marking a point on a number line. It just means to graph your line with respect to the x and y axes.
Definition of midpoint: a point, line, or plane that bisects a line so that AB=BC Midpoint theorem: a point, or plane that bisects a line so that line AB is congruent to line BC. A-----------------------------------------------B----------------------------------------------------C The definition of midpoint refers to equality, while midpoint theorem refers to congruency.
In plane geometry a line is a two dimentional object between two points. If a line or a point is not on the line it, by definition, does not contain them. The answer therefor is infinite. Unless it is a closed line which has a slightly different definition but the answer is the same.
When a line intersects a plane and does not lie in the plane, the intersection forms a single point. This point is where the line crosses the plane. If the line is parallel to the plane, however, there will be no intersection point.
The point of intersection of a tangent line or plane with a circle on a sphere is the single point where the line or plane touches the circle. This point is unique because, by definition, a tangent line or plane only intersects a circle at one point without passing through it. If the tangent is from an external point, it signifies that the line or plane is just "touching" the circle at that specific location. In three-dimensional space, this concept illustrates the relationship between the geometry of the sphere and the properties of tangents.
A dimension that exactly locates a reference point, reference line, or reference plane
Plane. A point has no dimension, a line has one dimension, and a plane has two dimensions.
point, line and plane
point * * * * * or, nothing (if the line is parallel to the plane).
plane
A ray
A plane intersects a line at a point, and i plane intersects another plane at a line.
The intersection of a line and a plane can result in either a single point, if the line passes through the plane, or no intersection at all if the line is parallel to the plane and does not touch it. In some cases, if the line lies entirely within the plane, every point on the line will be an intersection point. Thus, the nature of the intersection depends on the relative positions of the line and the plane.