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

Answer:

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

Step-by-step 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

  $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

  $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* 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 $(x_{2},y_{2})$

∴ $-3=\frac{-1(2)+x_{2}(1)}{1+2}$

∴ $-3=\frac{-2+x_{2}}{3}$

- Multiply both sides by 3

∴ $-9=-2+x_{2}$

- Add 2 for both sides

∴ $-7=x_{2}$

∴ $2=\frac{4(2)+y_{2}(1)}{1+2}$

∴ $2=\frac{8+y_{2}}{3}$

- 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)