Answer:
(d) 1 unit
Step-by-step explanation:
The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.
<h3>Original line segment</h3>
The length of the original horizontal line segment BC is the difference of its x-coordinates:
BC = 6 -4 = 2 . . . . units
(We know the segment is horizontal because the y-coordinates of the end points are the same.)
<h3>Dilated segment</h3>
Multiplying the length of the original segment by the dilation factor, we find the length of B'C':
B'C' = dilation factor × BC
B'C' = 0.5×(2 units)
B'C' = 1 unit
<h3>Dilated Coordinates</h3>
The dilation factor multiplies each coordinate value:
B' = 0.5B = 0.5(4, 3) = (2, 1.5)
C' = 0.5C = 0.5(6, 3) = (3, 1.5)
The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.
