Question

Hollis house is located at (-1,4). She can walk in a straight line to get to Jedds house. A fast food resturant is located at (-3,2) and partitions the way from hollis house to jedds house by a ration of 1:2 find the coordinates of jedds house

Answer 1

(-7 , -2)

Explanation:

The above answer is correct

Answer 2

The coordinates of Jedds house are (-7 , -2)

Explanation:

* Lets explain how to solve the problem

- If point (x , y) divide the distance between the two points

`(x_(1),y_(1))` and
`(x_(2),y_(2))` at the ratio

`(m_(1):m_(1))`, then

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

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

* Lets solve the problem

∵ Hollis house is located at (-1 , 4)

∴
`(x_(1),y_(1))` = (-1 , 4)

∵ She can walk in a straight line to get to Jedds house

∵ The restaurant is located at (-3 , 2) and partitions the way from

Hollis house to Jedds house by a ration of 1 : 2

∴ (x , y) = (-3 , 2)

∴
`(m_(1):m_(1))` = 1 : 2

- Lets consider that Jedds house is located at
`(x_(2),y_(2))`

∴
`-3=(-1(2)+x_(2)(1))/(1+2)`

∴
`-3=(-2+x_(2))/(3)`

- Multiply both sides by 3

∴
`-9=-2+x_(2)`

- Add 2 for both sides

∴
`-7=x_(2)`

∴
`2=(4(2)+y_(2)(1))/(1+2)`

∴
`2=(8+y_(2))/(3)`

- Multiply both sides by 3

∴
`6=8+y_(2)`

- Subtract 8 for both sides

∴
`-2=y_(2)`

∴ The coordinates of Jedds house are (-7 , -2)