Question

Holli's house is located at (−1, 4). She can walk in a straight line to get to Jedd's house. A fast food restaurant is located at (−3, 2) and partitions the way from Holli's house to Jedd's house by a ratio of 1:1. Find the coordinate of Jedd's house.

Answer 1

Answer:

The coordinates of Jedd's house is   (-5, 0)

Step-by-step explanation:

Given;

Location of Holli's House =  (−1, 4)

Location of  fast food restaurant = (−3, 2)

To Find:

The coordinate of Jedd's house.

Solution:

If  the distance between the two points   $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is divided by the point (x,y) in the ratio of m : n then

$x=\frac{x_{1}n+x_{2}m}{m + n}$

$y=\frac{y_{1}n+y_{2}m}{m + n}$

Hollis house is located at (-1 , 4)

So, $(x_{1},y_{1}) = (-1 , 4)$

She  walks in a straight line to get to Jedds house

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

(x , y) = (-3 , 2)

The ratio of  Hollis house to Jedds house  is 1 : 1

 (m : n) = 1 : 2

Lets consider that Jedds house is located at $(x_{2},y_{2})$

Then $x_2$ will be

$-3=\frac{-1(1)+x_{2}(1)}{1+1}$

$-3=\frac{-1 +x_{2}}{2}$

$-3 \times 2=-1 +x_{2}$

$-6 = -1 +x_{2}$

$-6 = -1 +x_{2}$

$-5 = x_{2}$

Now $y_{2}$ will be

$2=\frac{4(1)+y_{2}(1)}{1+1}$

$2=\frac{4+y_{2}}{2}$

$2 \times 2=4+y_{2}$

$4 = 4+y_{2}$

$4 - 4 = y_{2}$

$y_{2} = 0$

∴ The coordinates of Jedd's house is (-5, 0)