Question

Graph the image of this figure after a dilation with a scale factor of 3 centered at (−7, −6). Use the polygon tool to graph the dilated figure.

Answer 1

The dilation transformation gives an image that is similar to the pre-image

but have a different size.

• Please find attached the required graph of the image created with MS Excel

Reasons:

Points on the figure are; A(-7, -3), B(-3, -2), C(-4, -5)

The scale factor of dilation = 3

The center of dilation = (-7, -6)

Required:

The graph of the image following the dilation.

Solution:

The given points relative to the center of dilation are;

(-7 - (-7), -3 - (-6)) = (0, 3)

(-3 - (-7), -2 - (-6)) = (4, 4)

(-4 - (-7), -5 - (-6)) = (3, 1)

Following the dilation gives;

3 × (0, 3) = (0, 9)

3 × (4, 4) = (12, 12)

3 × (3, 1) = (9, 3)

Adding the coordinates of the center of dilation to the above relative points of the image gives;

Location of point A' = (0 + (-7) , 9 + (-6)) = (-7, 3)

Location of point B' = (12 + (-7) , 12 + (-6)) = (5, 6)

Location of point C' = (9 + (-7) , 3 + (-6)) = (2, -3)

Therefore, the image is; A'(-7, 3), B'(5, 6), C'(2, -3)

Learn more about dilation transformation here:

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