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Perpendiculars and Distance

•

Find the distance between a point and a line.

•

Find the distance between parallel lines.

Vocabulary

does the distance between

does the distance between

parallel lines relate to

parallel lines relate to

•

equidistant

hanging new shelves?

hanging new shelves?

When installing shelf brackets, it is

important that the vertical bracing be

parallel in order for the shelves to line

up. One technique is to install the first

brace and then use a carpenter’s square to measure and mark two or more

points the same distance from the first brace. You can then align the second

brace with those marks.

DISTANCE FROM A POINT TO A LINE

In Lesson 3-5, you learned that if

two lines are perpendicular to the same line, then they are parallel. The carpenter’s

square is used to construct a line perpendicular to each pair of shelves. The space

between each pair of shelves is measured along the perpendicular segment. This

is to ensure that the shelves are parallel. This is an example of using lines and

perpendicular segments to determine distance. The shortest segment from a point

to a line is the perpendicular segment from the point to the line.

Distance Between a Point and a Line

• Words

• Model

C

The distance from a line to

shortest

a point not on the line is

distance

the length of the segment

perpendicular to the line

from the point.

A

B

Study Tip

Distance from a Point to a Line

Example

Example

1

1

Measuring the

Shortest Distance

Draw the segment that represents

P

You can use tools like the

the distance from P to AB.

corner of a piece of paper

or your book to help draw

A

B

a right angle.

Since the distance from a line to a point not on the line is

P

the length of the segment perpendicular to the line from

the point, extend AB and draw PQ so that PQ

AB.

A

B

Q

When you draw a perpendicular segment from a point to a line, you can

guarantee that it is perpendicular by using the construction of a line perpendicular

to a line through a point not on that line.

Lesson 3-6 Perpendiculars and Distance 159

Aaron Haupt

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Parent category: Education