Question bank: Point, Line, and Plane

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Question 1:

Medium

Imagine you are working as an architect on a construction project. To plan the structure of a building, you must rely on the concepts of point, line, and plane. a) Define each of these concepts and explain their importance in the intended building project. b) Taking a point A and a line r that does not contain point A, describe how to draw a line s parallel to line r and passing through point A, applying Euclid's postulates. c) Analyzing two distinct planes, how can you determine if they are parallel or intersecting in your project?

Point, Line, and Plane

Question 2:

Medium

Point, Line, and Plane

Question 3:

Very Easy

An architect is designing a building and needs to establish a connection between two points A and B on the ground for the construction of a new structure. Points A and B are marked on the ground and must be connected by a road that will be represented by a straight line. Considering that there are no obstacles on the ground that prevent the construction of a straight line between A and B and that, according to Euclid's postulates, through a point outside a line passes one and only one line parallel to the given line, determine if it is possible to draw a line parallel to the line connecting points A and B on the ground, passing through point C which is 2 meters from A and 3 meters from B.

Point, Line, and Plane

Contextualized Question

Calculus Question

Question 4:

Very Hard

Consider a point P in the plane that does not belong to a line r. Let S be the set of all points in the plane that are symmetric to P with respect to r. Prove that S is a line and determine its position relative to r. Furthermore, prove that for any point Q belonging to S, the line passing through Q and parallel to r contains exactly one point of intersection with r.

Point, Line, and Plane

Theorical Question

Contextualized Question

Question 5:

Medium

In an archery competition, the target is located on a vertical plane. The line that the archer makes when aiming forms a straight line that intersects this plane at the point where the arrow hits the target. If the line that the archer makes when aiming forms an angle of 30 degrees with the horizontal plane and the archer is 20 meters away from the target, what is the height of the point on the vertical plane where the arrow hit the target?

Point, Line, and Plane

IARA TIP

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