A point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 5:1 ratio. Find M. You must show all work to receive credit. Also please put an ACTUAL answer, k tyy!

(8.5, 2.16666)

Step-by-step explanation:

10 - 1 = 9

x = 9/6 parts = 1.5

1.5(5) = 7.5

1 + 7.5 = 8.5

3 - -2 = 5

y = 5 / 6 parts = 5/6

5/6(5) = 25/6 = 4.166666

-2 + 4.1666666 = 2.166666

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.