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
[tex]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[/tex]
The coordinates of Cristian's house are: (13,-1) ..
Answer:
Step-by-step explanation:
Givens
The formula to solve this problem is
[tex]x=\frac{mx_{2}+nx_{1} }{m+n} \\y=\frac{my_{2}+ny_{1} }{m+n}[/tex]
Where
[tex]x=11\\y=0[/tex]
[tex]x_{1} =1\\y_{1}=5\\ x_{2}=?\\ y_{2} =?\\m=5\\n=1[/tex]
Replacing all these values, we have
[tex]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[/tex]
[tex]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[/tex]
Therefore, the Cristian's house is at (13, -1).
