Question bank: Point, Line, and Plane

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Question 1:

Medium

In a Cartesian coordinate system presented on the plane, Letícia chose the point A(2, 3) and the point B(6, 7). She wants to determine the equation of the line that passes through both points. What is the equation of the line that passes through points A and B?

Point, Line, and Plane

Question 2:

Medium

Imagine you are designing a skate park and need to create a ramp on an inclined plane. The coordinates of the three non-collinear points are A(0, 0, 0), B(1, 2, 3), and C(2, 4, 6). (a) Determine the general equation of the plane containing points A, B, and C. (b) Find the equation of the line that is the intersection between the plane determined in item (a) and the xy plane (z = 0). (c) Calculate the angle between the line found in item (b) and the xy plane.

Point, Line, and Plane

Question 3:

Medium

Imagine you are working on a design project and need to create a map representing the layout of three buildings aligned in a straight line, as points A, B, and C. Additionally, you need to verify that the available parking, identified as point D, does not belong to this line of buildings.

Point, Line, and Plane

Question 4:

Medium

Consider a point P and a line r in a plane, and a point Q outside the line r. Based on Euclid's postulates, it is known that through a point outside a line, only one line parallel to the given line passes. Demonstrate, using mathematical arguments and without the use of coordinates, why the statement 'through a point outside a line, only one line parallel to the given line passes' is true. Use your demonstration to justify why the statement is independent of the distance between points P and Q and the orientation of line r in the plane.

Point, Line, and Plane

Theorical Question

Contextualized Question

Question 5:

Very Easy

If two lines are not parallel and are in the same plane, we have that these lines are:

Point, Line, and Plane

Theorical Question

IARA TIP

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