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 1:2. Find the coordinate of Jedd's house.

Answer 1

Answer:

The coordinate of Jedd's house is:

                          (-7,-2)

Step-by-step explanation:

We know that if a Point P(a,b) partitions the line joining the point (x,y) and (x',y') in the ratio m:n

Then the coordinates of the point P is given by:

$a=\dfrac{mx'+nx}{m+n},\ b=\dfrac{my'+ny}{m+n}$

Here m:n=1:2

and (a,b)=(-3,2) i.e. location of the food restaurant.

and

(x,y)=(-1,4) i.e. location of Holli's house.

and (x',y') is the location of Jedd's house.

Hence, we have:

$-3=\dfrac{1\times x'+2\times (-1)}{1+2}\ and\ 2=\dfrac{1\times y'+2\times 4}{1+2}\\\\i.e.\\\\-3=\dfrac{x'-2}{3}\ and\ 2=\dfrac{y'+8}{3}\\\\i.e.\\\\-3\times 3=x'-2\ and\ 2\times 3=y'+8\\\\i.e.\\\\-9=x'-2\ and\ 6=y'+8\\\\i.e.\\\\x'=-9+2\ and\ y'=6-8\\\\i.e.\\\\x'=-7\ and\ y'=-2$

Answer 2

Answer:

Step-by-step explanation:

The coordinate of Jedd's house is:

                         (-7,-2)

Step-by-step explanation:

We know that if a Point P(a,b) partitions the line joining the point (x,y) and (x',y') in the ratio m:n

Then the coordinates of the point P is given by:

Here m:n=1:2

and (a,b)=(-3,2) i.e. location of the food restaurant.

and

(x,y)=(-1,4) i.e. location of Holli's house.

and (x',y') is the location of Jedd's house.

Hence, we have: