In a geometry class, students are asked to describe the dimensions of a plane based on the components that create a plane. which student’s response is correct? mark states that a plane has zero dimensions because it is made up of three noncollinear points. stacy states that a plane has two dimensions because it is made up of an infinite number of lines. dewayne states that a plane has one dimension because it contains the line intersecting two points. candice states that a plane can have multiple dimensions depending on how many points are labeled.

Question: In a geometry class, students are asked to describe the dimensions of a plane based on the components that create a plane. which student’s response is correct? mark states that a plane has zero dimensions because it is made up of three noncollinear points. stacy states that a plane has two dimensions because it is made up of an infinite number of lines. dewayne states that a plane has one dimension because it contains the line intersecting two points. candice states that a plane can have multiple dimensions depending on how many points are labeled.

In this blog post, we will explore a common question that students may encounter in a geometry class: how to describe the dimensions of a plane based on the components that create a plane. A plane, in geometry, is a flat, two-dimensional surface that extends indefinitely . It has no width or thickness. A plane can be defined by three non-collinear points (points that do not lie on the same line), a point and a line not on that line, two distinct intersecting lines, or two distinct parallel lines.

To understand the dimensions of a plane, we need to know what a dimension is. A dimension is a measure of how many coordinates are needed to specify a point on an object. For example, a point has zero dimensions, because it has no size and only needs one coordinate to locate it. A line has one dimension, because it has length but no width or thickness, and needs two coordinates to locate a point on it. A plane has two dimensions, because it has length and width but no thickness, and needs three coordinates to locate a point on it.

Now let's look at the responses of four students who are asked to describe the dimensions of a plane based on the components that create a plane.

- Mark states that a plane has zero dimensions because it is made up of three noncollinear points. This is incorrect, because three noncollinear points only define a plane, but do not make up the whole plane. There are infinitely many other points on the plane that are not defined by the three points. A plane has two dimensions, not zero.

- Stacy states that a plane has two dimensions because it is made up of an infinite number of lines. This is correct, because each line on the plane has one dimension, and there are infinitely many lines on the plane in different directions. The combination of these lines gives the plane two dimensions: length and width.

- Dewayne states that a plane has one dimension because it contains the line intersecting two points. This is incorrect, because the line intersecting two points is only one component of the plane, not the whole plane. There are infinitely many other lines on the plane that are not parallel to the given line. A plane has two dimensions, not one.

- Candice states that a plane can have multiple dimensions depending on how many points are labeled. This is incorrect, because labeling points does not change the nature of the plane or its dimensions. A plane always has two dimensions, regardless of how many points are labeled or how they are arranged.

Therefore, the correct answer is Stacy's response: a plane has two dimensions because it is made up of an infinite number of lines.

Rjwala

Rjwala is your freely Ai Social Learning Platform. here our team solve your academic problems daily.