Question

1. lynda plans to go to the animal shelter to adopt a dog and then take the dog to precious pup grooming services. the shelter is located at (-1, 9), while precious pup grooming services is located at (11, 0). find the location of lyndas home if it is ⅓ of the distance from the shelter to precious pup grooming services. the location of lyndas home is ( _, _).

Explanation:

Step1: Use the section - formula

Let the shelter be point $A(-1,9)$ and the grooming services be point $B(11,0)$. If a point $P(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$, the coordinates of $P$ are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$ and $n = 3 - 1=2$.

Step2: Calculate the $x$ - coordinate

$x=\frac{1\times11+2\times(-1)}{1 + 2}=\frac{11-2}{3}=\frac{9}{3}=3$.

Step3: Calculate the $y$ - coordinate

$y=\frac{1\times0+2\times9}{1 + 2}=\frac{0 + 18}{3}=6$.

Answer:

$(3,6)$