IXL - Dilations and parallel lines (Geometry practice)

Line

has the equation

–

Write the equation of the image of

after a dilation with a scale factor of 4, centered at the origin.

Write your answer in slope-intercept form.

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Learn with an example

question

Line

has the equation

Write the equation of the image of

after a dilation with a scale factor of 5, centered at the origin.

Write your answer in slope-intercept form.

key idea

The image of a line after a dilation is also a line.

The image of the point

(

)

dilated with a scale factor of

centered at the origin is

(

)

solution

You want to find the equation of the image of

after a dilation with a scale factor of 5, centered at the origin. Call this image

To find the equation of

you need two points that lie on

Begin by finding two points that lie on

Start with the

-intercept.

Since the equation of

in slope-intercept form is

which can be written as

the

-intercept

(

)

In other words,

passes through the origin, which is the center of the dilation.

Next, since the slope of

move up 1 and right 3 from

(

)

to find a second point on

(

)

So, the points

(

)

and

(

)

lie on

To find two points on

apply the dilation

(

)

↦

(

)

(

)

↦

(

)

(

)

↦

(

)

The image of the

-intercept

(

)

which is the y-intercept of

In general, the

-intercept

of a line's image after a dilation centered at the origin is the image of the

-intercept

of the original line. This is because the

-coordinate

of the

-intercept

is 0, so multiplying by the scale factor of the dilation does not change its value.

Next, use the slope formula to find the slope of

Slope of

Slope formula

–

Slope formula

Plug in

and

–

Plug in

and

Subtract

Simplify

So, the equation of

in slope-intercept form is

which is the equation of

In general, if a line passes through the center of the dilation, then it is the same as its image.

Looking for more? Try these:

Lesson: Dilations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

I.2Dilations: find the coordinates

E.3Equations of lines

Lesson: Dilations

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