perpendicular relacionships (1)

7/28/2019 Perpendicular Relacionships (1)

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D A R I O L O P E Z

C R I S T I A N P A E ZL A U R A P A R E D E S M I G U E L P O R T I L L O

PERPENDICULAR RELACIONSHIPS:

LINES AND PLANES

ENGINEERING FACULTY

MECHANICAL AND MECHATRONICS DEPARTMENT

BASIC DRAW

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CONTENTS

INTRODUCCION

PROJECTION OF A POINT ON A PLANE

PROJECTION OF A LINE ON A PLANE

SHORTEST DISTANCE FROM A POINT TO A LINE

TO DRAW A LINE PERPENDICULAR TO A PLANE

SHORTEST GRADE LINE FROM A POINT TO A

PLANE

TO DRAW A PLANE TROUGH A GIVEN POINT

AND PERPENDICULAR TO A GIVEN LINE

TO DRAW A PLANE TROUGH A GIVEN LINE ANDPERPENDICULAR TO A GIVEN PLANE

TO DRAW A PLANE TROUGH A GIVEN POINT

PERPENDICULAR TO EACH OF TWO GIVEN

PLANES

Bogot D.C., May 23th 2013

1.)

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PERPENDICULARITY

A line is said tobe perpendicular to

a plane if

1) the line intersectsthe plane

2) the line is notcompletelycontained in theplane

3) the line isperpendicular tosome line in theplane

Relationshipbetween two

geometric objectsthat meet ata right angle.


2.)

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PROJECTION OF A POINT ON A

PLANE


1. 2 views of a plane, project the point on

the plane

2.Draw two horizontal lines in each view.

3. Projecting the lines in true length

4. Draw a line that contains the point and

perpendicular to the line in true length.

5. The built line is projected

6. Project the point in the line

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PROJECTION OF A LINE ON A

PLANE

Bogot D.C., May 23th2013

1. Top and front views of a plane, project

the line on the front view plane

2. Drawn a line of immersion.

3.

With the line of immersion, we project theplane as edge

4. Draw a line perpendicular, to the line of

immersion and parallel the plane. After it is

projected and this indicate the location

the line in the edge view plane

5. Moving the length, the line is projected inthe other view.

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SHORTEST DISTANCE FROM A

POINT TO A LINE


1. 2 views of the line AB and the point C

2. Projecting the line AB in true length.

3. After this, project the line AB as a point

4. Take the distance from point C to line

AB.

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TO DRAW A LINE

PERPENDICULAR TO A PLANE


1. 2 views of a plane ABC and the point X

2. Draw the immersion line in front view

and project it in the top view.

3. Project the plane ABC as edge

4. Draw a perpendicular line from point X

until plane ABC

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SHORTEST GRADE LINE FROM A

POINT TO A PLANE


1. The top and front views of plane ABCand the point X are given.

2.Draw the auxiliary view that shows the

point X and the edge view of plane ABC

.3. Drawing a parallel from the point X to

the edge of the plane, then draw a line

with a decline of 30%

4. Lines XD and XE are projected in front

view

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TO DRAW A PLANE THROUGH A GIVEN

POINT AND PERPENDICULAR TO A

LINE


1. There are the two views (top and front)of the line AB and point X

2. From the point X draw a horizontal line

of indefinite length XY, it is projected in the

top view which appears true length and

perpendicular to AB

.3. After this point X is drawn from the topview a horizontal line of indefinite length,

XZ. View is projected to the front where itwill be perpendicular to AB and truelength.

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LINE AND PERPENDICULAR TO A

PLANE

1. The top and front views of plane ABCand the line XY are given.

2. Draw two horizontal lines on the plane in

each view.

3. The lines must be projected in its truelongitude, and is must be extended

4. From one end of the line XY draw a

perpendicular line until extended line

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POINT PERPENDICULAR TO EACH

OF GIVEN PLANES1. There are the two views (top and front)of the planes ABC and DEF, and the pointX

2. Draw horizontal lines in all views..

3. Projecting all the lines in its true length

4. Draw a line until point X from the

interceptions in each view.

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BIBLIOGRAPHY


HAWK, MINOR CLYDE, Descriptive Geometry, United States Of America, McGrawHill

Book Company, 1962.

Images taken from:

1). http://www.picthisposters.com/perpendicular.html

2). http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm

3). http://www.seduquere.com/espanol/web/bibliografiadeinteres.asp

3.)

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PROBLEMS

Determine the true length, slope, andbearing of the shortest distance from pointX to line AB. Show The shortest distance as a

line in all views.

A (3,5,4)

B (7,1,2)X (5.5,4, 5)

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PROBLEMS

This figure shows aplane ABCD,represented byparallel lines. Scale1:2. Find the shortesthorizontal distancefrom X to the plane.Also determine the

shortest line from X tothe plane and having35 % grade.

Bogot D.C., May 23th2013

2 cm10 cm 10 cm

6cm

12cm

8cm

4cm

8cm

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perpendicular relacionships (1)

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