Line segment AB has endpoints A (−1.5, 0) and B (4.5, 8). Point C is on line segment AB and is located at (0, 2).
What is the ratio of AC/CB?
Hint: Your answer should include these three parts. Use the distance formula to find AC. Then use the
distance formula to find CB. Write the lengths as a ratio, AC/CB.
To find the ratio of AC to CB, we first need to calculate the lengths of AC and CB.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the length of AC:
AC = sqrt((0 - (-1.5))^2 + (2 - 0)^2)
= sqrt((1.5)^2 + 2^2)
= sqrt(2.25 + 4)
= sqrt(6.25)
= 2.5
Next, we can find the length of CB:
CB = sqrt((4.5 - 0)^2 + (8 - 2)^2)
= sqrt(4.5^2 + 6^2)
= sqrt(20.25 + 36)
= sqrt(56.25)
= 7.5
Finally, we can find the ratio of AC to CB:
AC/CB = 2.5/7.5
= 1/3
Therefore, the ratio of AC to CB is 1/3.