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

(-5,0) is correct!!

Step-by-step explanation:.

Answer 2

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=(x_(1)n+x_(2)m)/(m + n)`

`y=(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=(-1(1)+x_(2)(1))/(1+1)`

`-3=(-1 +x_(2))/(2)`

`-3 * 2=-1 +x_(2)`

`-6 = -1 +x_(2)`

`-6 = -1 +x_(2)`

`-5 = x_(2)`

Now
`y_(2)` will be

`2=(4(1)+y_(2)(1))/(1+1)`

`2=(4+y_(2))/(2)`

`2 * 2=4+y_(2)`

`4 = 4+y_(2)`

`4 - 4 = y_(2)`

`y_(2) = 0`

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