Question

1. multiple choice find point r on st such that the ratio of sr to rt is 1:2. (lesson 1 - 6)

s(-6,8)
t(3,2)
a r(-5,6)
b r(-3,6)
c r(-1.5,5)
d r(0,4)

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 alonso’s 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)
3. multiple choice find the measure of yz if y is the midpoint of xz. (lesson 1 - 7)

x 12 - x
y 3x + 4
z
a 2
b 10
c 16
d 20

1. multiple choice find the y - coordinate of the point m, the midpoint of ab, for a(-3,3) and b(5,7). (lesson 1 - 7)

a -1
b 1
c 2
d 5

1. multiple choice points a and b are plotted on a number line. what is the location of m, the midpoint of ab, for a at -9 and b at 28? (lesson 1 - 7)

a m is located at 18.5 on the number line.
b m is located at 14 on the number line.
c m is located at 9.5 on the number line.
d m is located at 10/3 on the number line.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For a point that divides a line segment in the ratio $m:n$ from $(x_1,y_1)$ to $(x_2,y_2)$, the coordinates are given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$.

Step2: Solve problem 12

Given $S(-6,8)$ and $T(3,2)$ and the ratio $SR:RT = 1:2$.
$x_R=\frac{1\times3+2\times(-6)}{1 + 2}=\frac{3-12}{3}=\frac{-9}{3}=-3$
$y_R=\frac{1\times2+2\times8}{1 + 2}=\frac{2 + 16}{3}=\frac{18}{3}=6$
So $R(-3,6)$.

Step3: Solve problem 15

Since $Y$ is the mid - point of $\overline{XZ}$, then $12−x=3x + 4$.
Solve for $x$:
$12-4=3x+x$
$8 = 4x$
$x = 2$
$YZ=3x + 4=3\times2+4=10$

Step4: Solve problem 16

For $A(-3,3)$ and $B(5,7)$, the $y$ - coordinate of the mid - point $M$ is $\frac{3 + 7}{2}=5$

Step5: Solve problem 17

For $A=-9$ and $B = 28$, the mid - point $M$ is $\frac{-9+28}{2}=\frac{19}{2}=9.5$

Answer:

1. B. $R(-3,6)$
2. B. 10
3. D. 5
4. C. $M$ is located at 9.5 on the number line.