Question

point A is locatee at (2,8) and point B is located at (8,5). what point partitions the directed line segment AB into a 1:3 ratio​

Answer 1

The point is (3.5 , 7.25)

Explanation:

∵ A = (2 , 8) and B = (8 , 5)

∵ Let point P divides AB into a ratio 1:3

∵
`x=(m_(2)x_(1)+m_(1)x_(2))/(m_(1)+m_(2))`

∵
`y=(m_(2)y_(1)+m_(1)y_(2))/(m_(1)+m_(2))`

∴ x-coordinate of P = (2)(3) + (8)(1)/3 + 1 = (6 + 8)/4 = 3.5

∴ y-coordinate of P = (8)(3) + (5)(1)/1 + 3 = (24 + 5)/4 = 7.25

∴ P = (3.5 , 7.25)

Answer 2

point(3.5 , 7.25)

Explanation:

Given in the question,

pointA(2,8)

pointB(8,5)

To find,

A point which partition AB into 1:3

x1 = 2

x2 = 8

y1 = 8

y2 = 5

a = 1

b = 3

Formula to use

x' = x1 + (a/a+b)(x2-x1)

y' = y1 + (a/a+b)(y2-y1)

Plug in the values

x' = 2 + (1/1+3)(8-2)

= 3.5

y' = 8 + (1/1+3)(5-8)

= 7.25

So, point(3.5 , 7.25) partitions the directed line segment AB into a 1:3 ratio​