Question

How does dilation affect the length of line?

Answer 1

Hint: Now dilation of a line segment is a new line segment such that the new line is formed by the image points of the original points. The length of the new line is given by the length of original line segment multiplied by factor of dilation.

Complete step by step solution:
Now let us understand the concept of dilation.
Dilation is nothing but a transformation in the XY plane or XYZ plane.
Now let us first understand how this transformation happens. To do so we need a reference point. This is a fixed point in the plane and is called center of scaling. Now let us say we have a point O which is the center of scaling. Now let us say we want to transform point P in the plane. The Image of point P is obtained by shifting the original line OP such that the line OP’ is \[\left| OP' \right|=\left| f \right|\left| OP \right|\] where P’ is the image of point P and f is the scaling factor of dilation.
Hence if f > 1 then the length of the new segment will be greater than the original segment. Similarly if f < 1 then the length of the new segment is less than the original segment.

Note: Now note that if f > 0 then the image point will be on the same side as the original point with respect to center of scaling. Similarly if f < 0 then the image point and original point will be on opposite sides with respect to center of scaling.