Question

Segment AB has endpoints AC 4, 16) and B(8,0). The segment is dilated about the origin by a scale factor of 0.25 to create segment AB What are the endpoints of segment A'B'?

Answer 1

Given the endpoints of the segments to be (-4,16) and (8,0)

And also a scale factor of 0.25.

Step 1: Let's first try to convert 0.25 to fraction, for easy calculation

`\begin{gathered} 0.25\text{ =}(25)/(100) \\ \\ (25)/(100)\text{ = }(1)/(4) \end{gathered}`

Step 2: we will then multiply the coordinates given by the scale factor to get the dilated coordinates(A'B')

`\begin{gathered} (1)/(4)\text{ X (-4,16) =(-}(4)/(4),(16)/(4)\text{)} \\ (-1,4) \end{gathered}`

That of the second coordinate will be

`\begin{gathered} (1)/(4)\text{ X (8, 0) =(}(8)/(4),(0)/(4)\text{)} \\ \\ =\text{ (2,0)} \end{gathered}`

Hence, the dilated coordinate (A'B' ) of the segment will be => (-1,4) and (2,0)