Question

Jayda's house is located at (1, 5). She can walk in a straight line to get to Cristian's house. A fast-food restaurant is located at (11, 0) and partitions the way from Jayda's house to Cristian's house by a ratio of 5:1. Find the coordinate of Cristian's house.
Help Me . Im a little stuck

Answer 1

Answer:

(13, -1).

Step-by-step explanation:

Givens

• Jayda's house is at (1,5).
• The fast-food restaurant is at (11,0).
• The ratio of the partion is 5:1.

The formula to solve this problem is

$x=\frac{mx_{2}+nx_{1} }{m+n} \\y=\frac{my_{2}+ny_{1} }{m+n}$

Where

$x=11\\y=0$

$x_{1} =1\\y_{1}=5\\ x_{2}=?\\ y_{2} =?\\m=5\\n=1$

Replacing all these values, we have

$x=\frac{mx_{2}+nx_{1} }{m+n} \\11=\frac{5x_{2}+1(1) }{5+1}\\66=5x_{2}+1\\ 66-1=5x_{2}\\x_{2}=\frac{65}{5}= 13$

$y=\frac{my_{2}+ny_{1} }{m+n}\\0=\frac{5y_{2}+1(5) }{5+1}\\0=5y_{2} +5\\y_{2}=\frac{-5}{5}=-1$

Therefore, the Cristian's house is at (13, -1).

Answer 2

Answer:

(13,-1)

Step-by-step explanation:

Let the coordinates of Jayda's house be point A

So,

A(x_1,y_1) = (1,5)

Let the coordinates of Cristian's house be point B

So,

(x_2, y_2)

Let M denote the fast food restaurant

(x_M,y_M) = (11,0)

The ratio is 5:1

So,

m=5 and n=1

We have to find the coordinates of B

$x_M=\frac{nx_1+mx_2}{m+n} \\11=\frac{(1)(1)+(5)(x_2)}{1+5}\\ 11=\frac{1+5x_2}{6} \\11*6=1+5x_2\\66=1+5x_2\\66-1=5x_2\\65=5x_2\\x=13\\y_M=\frac{ny_1+my_2}{m+n}\\0=\frac{(1)(5)+5y_2}{1+5}\\0=\frac{5+5y_2}{6} \\0=5+5y_2\\-5 = 5y_2\\y_2 = -1$

The coordinates of Cristian's house are: (13,-1) ..