Question
If the line represented by y = -1/4x - 2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?
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The dilated line equation can be found by multiplying the coefficients of x and y by the scale factor of 4. This gives:
y = -4 * (1/4)x - 4(2)
Simplifying this expression, we get:
y = -x - 8
Therefore, the dilated line passes through the point (0, -8) and has a slope of -1.
The image of the original line under the dilation is a line with the same slope but four times farther from the origin. Therefore, the true statement about the image is:
The dilated line passes through the point (0, -8) and is four times farther from the origin than the original line.
y = -4 * (1/4)x - 4(2)
Simplifying this expression, we get:
y = -x - 8
Therefore, the dilated line passes through the point (0, -8) and has a slope of -1.
The image of the original line under the dilation is a line with the same slope but four times farther from the origin. Therefore, the true statement about the image is:
The dilated line passes through the point (0, -8) and is four times farther from the origin than the original line.