Question

find the midpoint of each line segment graphed below or with the given endpoints. show your work.
12)
13)
14)

1. (2,5), (-1,5)
2. (-8,-2), (-10,-4)
3. (-10,-10), (8,10)

find the other endpoint of the line segment with the given endpoint and midpoint.

1. endpoint: (-6,-2), midpoint: (9,-1)
2. endpoint: (3,8), midpoint: (9,0)
3. endpoint: (3,-9), midpoint: (6,-2)
4. endpoint: (-4,5), midpoint: (-3,1)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For finding the other endpoint given one endpoint $(x_1,y_1)$ and mid - point $(x_m,y_m)$, we use $x_2=2x_m - x_1$ and $y_2=2y_m - y_1$.

Step2: Solve for 15

For endpoints $(2,5)$ and $(-1,5)$, $x_m=\frac{2+( - 1)}{2}=\frac{1}{2}$, $y_m=\frac{5 + 5}{2}=5$. Mid - point is $(\frac{1}{2},5)$.

Step3: Solve for 16

For endpoints $(-8,-2)$ and $(-10,-4)$, $x_m=\frac{-8+( - 10)}{2}=-9$, $y_m=\frac{-2+( - 4)}{2}=-3$. Mid - point is $(-9,-3)$.

Step4: Solve for 17

For endpoints $(-10,-10)$ and $(8,10)$, $x_m=\frac{-10 + 8}{2}=-1$, $y_m=\frac{-10 + 10}{2}=0$. Mid - point is $(-1,0)$.

Step5: Solve for 18

Given endpoint $(-6,-2)$ and mid - point $(9,-1)$. $x_2=2\times9-( - 6)=24$, $y_2=2\times(-1)-( - 2)=0$. Other endpoint is $(24,0)$.

Step6: Solve for 19

Given endpoint $(3,8)$ and mid - point $(9,0)$. $x_2=2\times9 - 3=15$, $y_2=2\times0 - 8=-8$. Other endpoint is $(15,-8)$.

Step7: Solve for 20

Given endpoint $(3,-9)$ and mid - point $(6,-2)$. $x_2=2\times6 - 3=9$, $y_2=2\times(-2)-( - 9)=5$. Other endpoint is $(9,5)$.

Step8: Solve for 21

Given endpoint $(-4,5)$ and mid - point $(-3,1)$. $x_2=2\times(-3)-( - 4)=-2$, $y_2=2\times1 - 5=-3$. Other endpoint is $(-2,-3)$.

Answer:

1. $(\frac{1}{2},5)$
2. $(-9,-3)$
3. $(-1,0)$
4. $(24,0)$
5. $(15,-8)$
6. $(9,5)$
7. $(-2,-3)$