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Circle DD with a radius of 44 units is shown on a coordinate grid. Circle DD is dilated using a scale factor of 34\frac{3}{4}, centered at the origin, to map to Circle MM.

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Full solution

Q. Circle DD with a radius of 44 units is shown on a coordinate grid. Circle DD is dilated using a scale factor of 34\frac{3}{4}, centered at the origin, to map to Circle MM.
  1. Identify Radius and Scale Factor: Identify the original radius of Circle D and the scale factor for the dilation.\newlineCircle D has a radius of 44 units. The scale factor for the dilation is 34\frac{3}{4}.
  2. Apply Scale Factor: Apply the scale factor to the original radius to find the new radius of Circle M.\newlineTo find the new radius after dilation, we multiply the original radius by the scale factor.\newlineNew radius =Original radius×Scale factor= \text{Original radius} \times \text{Scale factor}\newlineNew radius =4 units×(34)= 4 \, \text{units} \times \left(\frac{3}{4}\right)
  3. Perform Multiplication: Perform the multiplication to calculate the new radius.\newlineNew radius = 44 units ×34=3\times \frac{3}{4} = 3 units
  4. Verify Calculation: Verify that the calculation is correct and makes sense in the context of the problem.\newlineThe new radius should be smaller than the original radius because the scale factor is less than 11. Since 33 units is less than 44 units, the calculation is reasonable.

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