Final answer:
To find the ratio AB/BC, first calculate the lengths of segments AB and BC using the distance formula, then divide the length of AB by the length of BC to get the ratio, which is 0.208.
Step-by-step explanation:
The question involves finding the ratio AB/BC where points A, B, and C lie on a straight line segment in the Cartesian plane with given coordinates A(-1,-3.5), B(0.2,-3), and C(5,1). To find the lengths of segments AB and BC, we can use the distance formula:
Distance formula:
The distance d between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)2 + (y2 - y1)2)
First, calculate the length of AB:
AB = √((0.2 - (-1))2 + (-3 - (-3.5))2)
= √((1.2)2 + (-0.5)2)
= √(1.44 + 0.25)
= √(1.69)
= 1.3
Then, calculate the length of BC:
BC = √((5 - 0.2)2 + (1 - (-3))2)
= √((4.8)2 + (4)2)
= √(23.04 + 16)
= √(39.04)
= 6.25
Finally, find the ratio AB/BC:
AB/BC = 1.3/6.25
= 0.208