Final answer:
After dilating the point (-8,0) by a scale factor of 1/4, centered at the origin, the image of the point becomes (-2,0).
Step-by-step explanation:
The question involves finding the image of a point after a dilation with a scale factor centered at the origin in a coordinate plane. In this case, the point (-8,0) is being dilated by a scale factor of ¼, which means each coordinate of the point is multiplied by ¼. To find the image of the point, multiply the x-coordinate and the y-coordinate by the scale factor.
The calculation for the x-coordinate is: -8 × ¼ = -2
The calculation for the y-coordinate is: 0 × ¼ = 0
Therefore, the image of (-8,0) after the dilation is (-2,0).