Question

Give the coordinates of point F are (2.25, 0.25), what is the ratio of CF to FD?

what is the ration if point c=( -6, 4) and d=(5,-1)

Answer 1

To find the ratio of CF to FD for points C = (-6, 4), D = (5, -1), and F = (2.25, 0.25), calculate the distances between the points and then divide them. The ratio CF to FD is approximately 3.01.

Step-by-step explanation:

To find the ratio of CF to FD given the points C = (-6, 4), D = (5, -1), and F = (2.25, 0.25), we first need to calculate the distances between these points using the distance formula d = √((x2 - x1)^2 + (y2 - y1)^2).

For CF, use the coordinates of C (-6,4) and F (2.25, 0.25):
d_{CF} = √((2.25 - (-6))^2 + (0.25 - 4)^2)
= √((2.25 + 6)^2 + (-3.75)^2)
= √(68.5625 + 14.0625)
= √(82.625)
= 9.09 approximately.

For FD, use the coordinates of F (2.25, 0.25) and D (5, -1):
d_{FD} = √((5 - 2.25)^2 + (-1 - 0.25)^2)
= √((2.75)^2 + (-1.25)^2)
= √(7.5625 + 1.5625)
= √(9.125)
= 3.02 approximately.

Now, the ratio of CF to FD is d_{CF} / d_{FD}
= 9.09 / 3.02
= 3.01 approximately.