a point q on a segment with endpoints a (2, −1) and c (4, 2) partitions the segment in a 4: 1 ratio. find q. you must show all work to receive credit.

point q: (3.6, 1.4)

step-by-step explanation:

when you need to find a point between 2 points, you can work with "x" and with "y" separately:

point a: (2, -1)

point c: (4, 2)

distance in x: (4-2) = 2

distance in y: ()) = 3

the point q partitions the segment in 4: 1, from that you can divide the segment in 5 parts.

each part in x = 2/5 = 0.4

each part in y = 3/5 = 0.6

i will assume that the 4 parts are from a to q (because it isnt specified in the problem)

q: point a + 4 parts:

point q: (2, -1) +(0.4*4, 0.6*4) = (3.6, 1,4)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)