Questions: A preimage includes a line segment with a length of x units and a slope of m units. The preimage is dilated by a scale factor of n. The length of the corresponding line segment in the image is units. The slope of the corresponding line segment in the image is .

Solution Steps

To solve this problem, we need to understand the effects of dilation on a line segment. Dilation affects the length of the line segment but does not change its slope. The length of the line segment in the image is the original length multiplied by the scale factor. The slope remains unchanged.

The length of the corresponding line segment in the image after dilation is calculated using the formula: \[ \text{Length in image} = x \cdot n \] Substituting the given values \( x = 5 \) and \( n = 3 \): \[ \text{Length in image} = 5 \cdot 3 = 15 \text{ units} \]

The slope of the corresponding line segment in the image remains unchanged during dilation. Therefore: \[ \text{Slope in image} = m \] Given \( m = 2 \): \[ \text{Slope in image} = 2 \]

Final Answer