Question

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:

(A) x
(B) nx
(C) x/n
(D) nx/2

Answer 1

After a preimage with a line segment of x units is dilated by a scale factor of n, the length of the resulting line segment in the image is nx. The slope does not affect the dilated line length.

Step-by-step explanation:

The student asked what is the length of the corresponding line segment in the image when a preimage with a line segment of x units is dilated by a scale factor of n. When you perform a dilation, which is a transformation that produces an image that is the same shape as the original, but is a different size, the length of the line segments are multiplied by the scale factor. Since the original line segment is x units in length, after dilation by a factor of n, the new length will be nx units.

The slope of a line (m) or the orientation of the line (whether it is upright or inverted) does not affect the length of the line segment after dilation, nor does it alter the scale factor. Only the scale factor n is used to calculate the dilated length, resulting in answer (B) nx. Dilating a figure by a factor of n scales all linear dimensions up or down by that factor, which means that distances, perimeters, and areas change proportionally.

Answer 2

The length of the line segment in the image after a dilation with scale factor n is nx units, which is option (B). The slope of the line does not change the effect of dilation.

Step-by-step explanation:

When a preimage undergoes a dilation with a scale factor of n, every length in the preimage is scaled by n. This means that a line segment with an original length of x units will have a length of nx units in the image after dilation. The slope of the line does not affect the dilation process; it remains consistent regardless of the scale factor applied to the lengths.

In summary, if we have a preimage with a line segment of x units and the preimage is dilated by a factor of n, the length of the corresponding line segment in the image would be option (B) nx units.