Answer :
The ratio of [tex]\frac{CB}{AC}[/tex] is 3.
How to calculate a distance ratio in a line segment
The ratio of [tex]\frac{CB}{AC}[/tex] is the length of line segment CB divided by line segment AC. Each length is found by Pythagorean theorem:
Line segment AC
[tex]AC = \sqrt{[2.5-(-2)]^{2}+(6-0)^{2}}[/tex]
[tex]AC = 7.5[/tex]
Line segment CB
[tex]CB = \sqrt{(4-2.5)^{2}+(8-6)^{2}}[/tex]
[tex]CB = 2.5[/tex]
Finally, the ratio of [tex]\frac{CB}{AC}[/tex] is:
[tex]\frac{CB}{AC} = \frac{2.5}{7.5}[/tex]
[tex]\frac{CB}{AC} = 3[/tex]
The ratio of [tex]\frac{CB}{AC}[/tex] is 3.
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