Respuesta :
The scale factor of dilation is 0.75
How to find the ?
given that
let the segment is denoted by AB.
The segment with endpoints (0, 8) and (-6, 0) is dilated to a segment with endpoints (0, 6) and (-4.5, 0).
The amount by which the figure is stretched or contracted in a dilatation is known as the scale factor.
The figure's size change is described by the scale factor of dilation.
now we find the scale factor of dilation.
so, the formula is
AB X k = A'B'
so now first find the length of segment AB with endpoints (0, 8) and (-6, 0).
[tex]d = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1)}^{2} } \\ d = \sqrt{ {( - 6 - 0)}^{2} + {(0 - 8)}^{2} } \\ d = \sqrt{ {( - 6)}^{2} + {( - 8)}^{2} } \\ d = \sqrt{36 + 64} \\ d = \sqrt{100} \\ d = 10[/tex]
now find the length of segment A'B' with endpoints (0, 6) and (-4.5, 0).
[tex]d = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1)}^{2} } \\ d = \sqrt{ {( - 4.5 - 0)}^{2} + {(0 - 6)}^{2} } \\ d = \sqrt{ {( - 4.5)}^{2} + {( - 6)}^{2} } \\ d = \sqrt{20.25 + 36} \\ d = \sqrt{56.25} \\ d = 7.5[/tex]
scale factor of dilation is
[tex] AB X k = A'B' \\ 10k = 7.5 \\ k = \frac{7.5}{10} \\ k = 0.75[/tex]
Hence, the scale factor of dilation is 0.75
Learn more about scale factor of dilation, refer:
https://brainly.com/question/3457976
#SPJ9
