Pergunta

Dilation D_(v)(2)/(5) was performed on a rectangle. How does the image relate to the pre-image? Select three option The image is a reduction because 0lt nlt 1 The side lengths of the image are two -fifths the size of the corresponding side lengths of the pre-image. The angles of the image are two-fifths the size of the angles of the pre-image. The center of dilation is at point Q. The base of the image is two-fifths the size of the base of the pre-image.
Solução

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RenanElite · Tutor por 8 anos
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To determine how the image relates to the pre-image after a dilation with a scale factor of $\frac{2}{5}$, let's analyze each option:<br /><br />1. **The image is a reduction because $0 < n < 1$**:<br /> - This statement is correct. Since the scale factor $\frac{2}{5}$ is between 0 and 1, the dilation results in a reduction.<br /><br />2. **The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image**:<br /> - This statement is correct. The scale factor $\frac{2}{5}$ means that each side length of the image is $\frac{2}{5}$ times the corresponding side length of the pre-image.<br /><br />3. **The angles of the image are two-fifths the size of the angles of the pre-image**:<br /> - This statement is incorrect. Dilation does not change the measures of the angles; they remain the same in both the pre-image and the image.<br /><br />4. **The center of dilation is at point Q**:<br /> - This statement cannot be determined from the given information. The center of dilation is not provided in the problem statement.<br /><br />5. **The base of the image is two-fifths the size of the base of the pre-image**:<br /> - This statement is correct. Since the scale factor is $\frac{2}{5}$, the base of the image is $\frac{2}{5}$ times the size of the base of the pre-image.<br /><br />Therefore, the correct options are:<br />- The image is a reduction because $0 < n < 1$.<br />- The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.<br />- The base of the image is two-fifths the size of the base of the pre-image.
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