A common application of coordinate dilations is displaying digital images on a computer monitor.

A computer monitor, or computer screen, contains a certain amount of pixels. A pixel is a point on the monitor that lights up with a particular color, depending on the program that is being run.

computer monitor with x-axis, y-axis, and pixel coordinates labeled

Pixels are given a location using Quadrant I of a coordinate plane. Computer programs use x- and y-coordinates to locate each pixel and assign it a particular color.

For example, the monitor shown in the picture has a horizontal dimension of 1366 pixels and a vertical dimension of 768 pixels. Each pixel on the monitor can be used to generate an image.

The pixel shown is 1200 pixels from the left-hand corner, or origin, and 721 pixels above the left-hand corner, or origin. It is the pixel located at the ordered pair (1200, 721).

Let’s see this in action. Adan is a computer programmer, and he wants to generate an animation sequence by enlarging a figure whose outline is the trapezoid shown on the graph below. He is using a computer monitor like the one shown before, with a horizontal dimension of 1366 pixels and a vertical dimension of 768 pixels. His computer screen and the outline of the image are shown on the graph below.

graph with trapezoid

This activity might not be viewable on your mobile device.Interactive exercise. Assistance may be required.First, let's practice with the following activity using scale factors to identify new coordinates. The slider on the left hand side changes the scale factor.

Use the information from the graph to fill in the chart below.

 

 

Point

Original Coordinates

Scale factor
1

Scale factor 1.5

Scale factor
2

Scale factor
2.5

Scale factor
3

A

 

 

 

 

 

 

B

 

 

 

 

 

 

C

 

 

 

 

 

 

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Check Your Answer

 

 

Point

Original Coordinates

Scale factor
1

Scale factor 1.5

Scale factor
2

Scale factor
2.5

Scale factor
3

A

(1,1)

(1,1)

(1.5,1.5)

(2,2)

(2.5,2.5)

(3,3)

B

(2,5)

(2,5)

(3,7.5)

(4,10)

(5, 12.5)

(6,15)

C

(4,1)

(4,1)

(6,1.5)

(8,2)

(10,2.5)

(12,3)

Close Pop Up

Study the table you created. Describe how the scale factor can be used to determine the new coordinates.

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Check Your Answer

The new x and y coordinates can be found by multiplying the original coordinates by the scale factor. Close Pop Up

Now that you practiced finding the coordinates using scale factors, go back to the graph showing the outline of the image Adan would like to enlarge.

computer monitor with x-axis, y-axis, and pixel coordinates labeled

Copy the table below in your notes, and fill in the blanks.

 

New Coordinates

Point

Original Coordinates

Scale factor
1.5

Scale factor
2

Scale factor
2.5

Scale factor
3

A

(120,50)

 

 

 

 

B

(120,200)

 

 

 

 

C

(360,200)

 

 

 

 

D

(360,100)

 

 

 

 

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Check Your Answer

 

New Coordinates

Point

Original Coordinates

Scale factor
1.5

Scale factor
2

Scale factor
2.5

Scale factor
3

A

(120,50)

(180, 75)

(240, 100)

(300, 125)

(360, 150)

B

(120,200)

(180, 300)

(240, 400)

(300, 500)

(360, 600)

C

(360,200)

(540, 300)

(720, 400)

(900, 500)

(1080, 600)

D

(360,100)

(540, 150)

(720, 200)

(900, 250)

(1080, 300)

Close Pop Up

 


Practice

Pentagon ABCDE is the outline of a figure on a computer screen. The pixels representing the vertices of the pentagon are shown below.

pentagon graphed on the coordinate plane
  1. If the figure is dilated by a scale factor of 0.6, what will be the coordinates of each new pixel?

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    Click for a hint

    Use the points to read the coordinates of each labeled point, and then use the scale factor to determine the coordinates of the new pixel. Close Pop Up

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    Check Your Answer

    A' (144, 120), B' (144, 300), C' (432, 420), D' (432, 240), and E' (288, 240) Close Pop Up

  2. If the original figure is dilated by a scale factor of 1 over 5 1 5 , what will be the coordinates of each new pixel?

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    Click for a hint

    Use the points to read the coordinates of each labeled point, and then use the scale factor to determine the coordinates of the new pixel. Close Pop Up

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    Check Your Answer

    A' (48, 40), B' (48, 100), C' (144, 140), D' (144, 80), and E' (96, 80) Close Pop Up

  3. Hexagon ABCDEF is the outline of a figure on a computer screen. The pixels representing the vertices of the pentagon are shown below.

    hexagon graphed on the coordinate plane
  4. If the original figure is dilated by a scale factor of 13 over 4 3 4 , what will be the coordinates of each new pixel?

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    Click for a hint

    Use the points to read the coordinates of each labeled point, and then use the scale factor to determine the coordinates of the new pixel. Close Pop Up

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    Check Your Answer

    A' (420, 700), B' (630, 525), C' (630, 350), D' (420, 175), E' (210, 350), and F' (210, 525) Close Pop Up

  5. Beatrix, the computer programmer, wants to dilate the figure using a scale factor of 225%. If she does, will the image still fit on the computer screen with dimensions of 1366 pixels by 768 pixels? How can you tell?

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    Click for a hint

    Use the points to read the coordinates of each labeled point, and then use the scale factor to determine the coordinates of the new pixel. Close Pop Up

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    Check Your Answer

    No. The coordinates of the new pixel represented by A' will be (540, 900), and 900 in the vertical direction is above the top of the screen, which is 768 pixels high. Close Pop Up