Rectangle BCDE is shown on the coordinate grid. Rectangle BCDE is dilated with the origin as the center of dilation using the rule (x, y) → (1/3x, 1/3y) to create rectangle B'C'D'E'.
Which of the following statements is true?
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a
Rectangle B'C'D'E' is larger than rectangle BCDE, because the scale factor is greater than 1
b
Rectangle B'C'D'E' is smaller than rectangle BCDE, because the scale factor is less than 1.
c
Rectangle B'C'D'E' is smaller than rectangle BCDE, because the scale factor is greater than 1.
d
Rectangle B'C'D'E' is larger than rectangle BCDE, because the scale factor is less than 1.
b. Rectangle B'C'D'E' is smaller than rectangle BCDE, because the scale factor is less than 1.
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To determine which of the given statements is true, we need to understand how dilation works and compare the scale factor.
In dilation, the original shape is enlarged or reduced by a scale factor. The scale factor determines whether the dilated shape will be larger or smaller than the original shape.
In this case, the rule given for dilation is (x, y) → (1/3x, 1/3y), which means that every x-coordinate and y-coordinate of the original shape will be multiplied by 1/3 to get the corresponding coordinates of the dilated shape.
Since the scale factor is 1/3, which is less than 1, we can conclude that the dilated shape will be smaller than the original shape. Therefore, the correct answer is:
b) Rectangle B'C'D'E' is smaller than rectangle BCDE, because the scale factor is less than 1.