Question

1. open response alonso 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) on the coordinate plane, while precious pup grooming services is located at (11, 0) on the coordinate plane. find the location of alonsos home if it is 1/3 of the distance from the shelter to precious pup grooming services. (lesson 1-6)
2. open response find the coordinates of a if m(6, -1) is the midpoint of ab, and b has the coordinates (8, -7). (lesson 1-7)

Explanation:

Step1: Recall section - formula

The formula for finding a point $P(x,y)$ that divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 1$, $n = 2$, $x_1=-1$, $y_1 = 9$, $x_2=11$, and $y_2 = 0$.

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

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

for question 14:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(6,-1)$ and $B(8,-7)$, let the coordinates of $A$ be $(x,y)$. Then $\frac{x + 8}{2}=6$ and $\frac{y+( - 7)}{2}=-1$.

Step2: Solve for the x - coordinate of A

$\frac{x + 8}{2}=6$, multiply both sides by 2: $x + 8=12$, subtract 8 from both sides: $x=12 - 8=4$.

Step3: Solve for the y - coordinate of A

$\frac{y-7}{2}=-1$, multiply both sides by 2: $y-7=-2$, add 7 to both sides: $y=-2 + 7=5$.

Answer:

$(3,6)$