If you want to dilate a square 6 units to create a square with a side of 18 units, what scale factor should you use?
To find the scale factor, we can divide the length of the side of the larger square by the length of the side of the smaller square.
Scale factor = 18 units / 6 units = 3
Therefore, you should use a scale factor of 3 to dilate the square.
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If you dilate a circle of radius 2 mm with a scale factor of 50, what will the radius of the dilated circus?
To find the radius of the dilated circle, we can multiply the original radius by the scale factor.
Radius of dilated circle = 2 mm * 50 = 100 mm
Therefore, the radius of the dilated circle will be 100 mm.
A quadrilateral has the following vertices: (4, 4), (6, 6), (8, 4), (6, 2). After dilation, the new quadrilateral has the following vertices: (3, 3), (4.5, 4.5), (6, 3), (4.5, 1.5).
To determine the scale factor used for the dilation, we can calculate the ratio of the corresponding side lengths of the original and dilated quadrilaterals.
Using the first pair of corresponding sides, we can find the scale factor between (4, 4) and (6, 6) and (3, 3) and (4.5, 4.5) respectively:
Length of original side = √[(6 - 4)^2 + (6 - 4)^2] = √8 = 2√2
Length of dilated side = √[(4.5 - 3)^2 + (4.5 - 3)^2] = √2.5 = (√(5/2))
Scale factor = Length of dilated side / Length of original side = (√(5/2)) / (2√2) = (√5) / (√8) = (√5) / (2√2) = (√5 / 2) * (√2 / √2) = (√10 / 4)
Therefore, the scale factor used for the dilation is (√10 / 4).
Similarly, we can calculate the scale factor between the remaining pairs of corresponding sides to verify that they all have the same scale factor.