IXL - Find the distance between two parallel lines (Geometry practice)

Line

ℓ

has the equation

–

and line

ℓ

has the equation

Find the distance between

ℓ

and

ℓ

Round your answer to the nearest tenth.

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Learn with an example

question

Line

ℓ

has the equation

and line

ℓ

has the equation

–

Find the distance between

ℓ

and

ℓ

Round your answer to the nearest tenth.

key idea

The distance between two parallel lines is the distance between one line and a point on the other line.

The distance between a point and a line is the length of the segment perpendicular to the line from the point.

solution

The line

ℓ

is a vertical line with an

-intercept

of 2. The line

ℓ

is a vertical line with an

-intercept

–

Since

ℓ

and

ℓ

are both vertical lines with different

-intercepts,

they are parallel.

To find the distance between

ℓ

and

ℓ

pick a point on one of the lines and find the distance from that point to the other line. For convenience, pick the

-intercept

ℓ

(

)

Call this point

Now, calculate the distance between

ℓ

and

The point

(

–

)

lies on

ℓ

and is directly to the left of

The segment perpendicular to

ℓ

from

is the horizontal segment between

and

which is

To find the distance between

ℓ

and

ℓ

find the length of

The length is the absolute value of the difference in

-coordinates

and

which is

–

So, the distance between

ℓ

and

ℓ

is 3.

Looking for more? Try these:

Lesson: Distance formula

Lesson: Equations of parallel and perpendicular lines

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Work it out

Not feeling ready yet? These can help:

E.6Find the distance between a point and a line

Lesson: Distance formula

Lesson: Equations of parallel and perpendicular lines

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