Point a is located at (0, 4), and point c is located at (−3, 5). find the x value for the point b that is located one fourth the distance from point a to point c. −0.25 −0.5 −0.75 −1

The value of x-coordinate of point B is -0.75 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to find a point divides a line into two parts with

 a given ratio

- If pont (x , y) divides a line segment whose endpoints are (x1 , y1)

 and (x2 , y2) at ratio m1 : m2 from point (x1 , y1) to point (x2 , y2),

 internally then

 and

* Lets solve the problem

- Point A = (0 , 4) and point C = (-3 , 5)

- Point B located one fourth the distance AC

∴ Point B divides the line segment AC at a ratio 1 : 3 from point A to

  point c internally (because one fourth from A to C means the line

  AC is 4 parts and AB is one of them, then BC will be 4 - 1 = 3)

- Lets use the rule above to find the x-coordinate of point B

∵ A = (0 , 4) and C = (-3 , 5)

∴ x1 = 0 and x2 = -3

∵ B divides segment AC at ratio 1 : 3 from A to C

∴ m1 = 1 and m2 = 3

- Lets use the rule of x above to find its value

∴

∴ The value of x-coordinate of point B is -0.75