Jayda's house is located at (1, 5). she can walk in a straight line to get to cristian's house. a fast-food restaurant is located at (7, 2) and partitions the way from jayda's house to cristian's house by a ratio of 3: 1. find the coordinate of cristian's house.
(3, 4)
(5, 3)
(9, 1)
(11, 0)

The coordinate of Cristian's house are (9 , 1) ⇒ 3rd answer

Step-by-step explanation:

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

- If point (x , y) divides a line whose endpoints are (x1 , y1) and (x2 , y2)

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

#

* Lets solve the problem

∵ Jayda's house is located at (1, 5)

∵ Cristian's house is located at (x2 , y2)

∵ A fast-food restaurant is located at (7, 2)

∵ A fast-food restaurant is at ratio 3 : 1 from Jayda's house to

  Cristian's house

- Lets use the rule above

∵ (x1 , y1) = (1 , 5)

∵ (x , y) = (7 , 2)

∵ m1 = 3 and m2 = 1

∴

∴ ⇒ by using cross multiplication

∴ 28 = 1 + 3 x2 ⇒ subtract 1 from both sides

∴ 27 = 3 x2 ⇒ divide both sides by 3

∴ 9 = x2

- Similar lets find y2

∵

∴ ⇒ by using cross multiplication

∴ 8 = 5 + 3 y2 ⇒ subtract 5 from both sides

∴ 3 = 3 y2 ⇒ divide both sides by 3

∴ 1 = y2

∵ Cristian's house is located at (x2 , y2)

∴ Cristian's house is located at (9 , 1)

* The coordinate of Cristian's house are (9 , 1)

step-by-step explanation: