Question

Which statements are true about collinear points? Select all that apply. A plane exists that contains all of the points. A line exists that contains all of the points. More than one plane exists that contains all of the points. More than one line exists that contains all of the points. Question 2 Which statements are true about coplanar points? Select all that apply. A plane exists that contains all of the points. A line exists that contains all of the points. More than one plane exists that contains all of the points. More than one line exists that contains all of the points.

Answer 1

Answer:

Explanation:

1 )

Statements that are true about collinear points :

A plane exists that contains all of the points.

A line exists that contains all of the points.

More than one plane exists that contains all of the points.

2 )

Statements that are true about coplanar points :

A plane exists that contains all of the points.

Answer 2

Question 1: Statements that are true about collinear points are:

• A plane exists that contains all of the points.
• A line exists that contains all of the points.
• More than one plane exists that contains all of the points.

Question 2:  The statements that is true about coplanar points is:

• A plane exists that contains all of the points

Collinear points are a group of points that lie on the same straight line, the property of this phenomenon is called collinearity. Collinear points may exist on different planes, but they must be on the same lines.

So any group of points will only be collinear if they exist on the same straight line. Any two points must always be collinear, as a straight line can connect them, but three or more points must not necessarily be collinear.

There are different methods through which it can be determined if lines are collinear or not, the most commonly used are:

• the distance formula, $d=\sqrt({x} _{2}-x_{1})^{2} + (y_{2} -y_{1})^{2}$

• the slope formula, $m= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

• the area of triangle formula,$A= \frac{1}{2} {x_{1} ({y} _{2}-y_{3}) + x_{2} (y_{3} -y_{1}) + x_{3} (y_{1} -y_{2}) = 0$

Coplanar points are a set of points that all lie on the same plane. While or three points are always coplanar, four or more points might not necessarily be coplanar.

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