Practice

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.

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.

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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)

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

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

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.

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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		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)

Original Coordinates

Scale factor
1

Scale factor 1.5

Scale factor
2

Scale factor
2.5

Scale factor
3

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

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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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.
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A' (144, 120), B' (144, 300), C' (432, 420), D' (432, 240), and E' (288, 240)
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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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.
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A' (48, 40), B' (48, 100), C' (144, 140), D' (144, 80), and E' (96, 80)

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

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