Question

the coordinates of the endpoints of a segment are given. find the coordinates of the midpoint of each segment. 10. (0, 10), (0, 0) 11. (8, 0), (0, 0) 12. (0, -6), (0, 0) 13. (-20, 0), (0, 0) 14. (4, 12), (8, 20) 15. (-2, 3), (2, 5) 16. (1, -6), (-5, -10) 17. (-5, -14), (-1, -8) 18. (-1, -15), (9, 15) 19. (7, 2), (-7, -2) 20. (7, -5), (3, 15) 21. (-9, 7), (3, 5) 22. (1, 3), (4, 8) 23. (-6, 7), (9, 10)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for problem 10

For points $(0,10)$ and $(0,0)$, $x_1 = 0,x_2 = 0,y_1 = 10,y_2 = 0$. Then the mid - point is $(\frac{0+0}{2},\frac{10 + 0}{2})=(0,5)$.

Step3: Solve for problem 11

For points $(8,0)$ and $(0,0)$, $x_1 = 8,x_2 = 0,y_1 = 0,y_2 = 0$. Then the mid - point is $(\frac{8 + 0}{2},\frac{0+0}{2})=(4,0)$.

Step4: Solve for problem 12

For points $(0,-6)$ and $(0,0)$, $x_1 = 0,x_2 = 0,y_1=-6,y_2 = 0$. Then the mid - point is $(\frac{0+0}{2},\frac{-6 + 0}{2})=(0,-3)$.

Step5: Solve for problem 13

For points $(-20,0)$ and $(0,0)$, $x_1=-20,x_2 = 0,y_1 = 0,y_2 = 0$. Then the mid - point is $(\frac{-20 + 0}{2},\frac{0+0}{2})=(-10,0)$.

Step6: Solve for problem 14

For points $(4,12)$ and $(8,20)$, $x_1 = 4,x_2 = 8,y_1 = 12,y_2 = 20$. Then the mid - point is $(\frac{4+8}{2},\frac{12 + 20}{2})=(6,16)$.

Step7: Solve for problem 15

For points $(-2,3)$ and $(2,5)$, $x_1=-2,x_2 = 2,y_1 = 3,y_2 = 5$. Then the mid - point is $(\frac{-2 + 2}{2},\frac{3+5}{2})=(0,4)$.

Step8: Solve for problem 16

For points $(1,-6)$ and $(-5,-10)$, $x_1 = 1,x_2=-5,y_1=-6,y_2=-10$. Then the mid - point is $(\frac{1+( - 5)}{2},\frac{-6+( - 10)}{2})=(-2,-8)$.

Step9: Solve for problem 17

For points $(-5,-14)$ and $(-1,-8)$, $x_1=-5,x_2=-1,y_1=-14,y_2=-8$. Then the mid - point is $(\frac{-5+( - 1)}{2},\frac{-14+( - 8)}{2})=(-3,-11)$.

Step10: Solve for problem 18

For points $(-1,-15)$ and $(9,15)$, $x_1=-1,x_2 = 9,y_1=-15,y_2 = 15$. Then the mid - point is $(\frac{-1 + 9}{2},\frac{-15+15}{2})=(4,0)$.

Step11: Solve for problem 19

For points $(7,2)$ and $(-7,-2)$, $x_1 = 7,x_2=-7,y_1 = 2,y_2=-2$. Then the mid - point is $(\frac{7+( - 7)}{2},\frac{2+( - 2)}{2})=(0,0)$.

Step12: Solve for problem 20

For points $(7,-5)$ and $(3,15)$, $x_1 = 7,x_2 = 3,y_1=-5,y_2 = 15$. Then the mid - point is $(\frac{7 + 3}{2},\frac{-5+15}{2})=(5,5)$.

Step13: Solve for problem 21

For points $(-9,7)$ and $(3,5)$, $x_1=-9,x_2 = 3,y_1 = 7,y_2 = 5$. Then the mid - point is $(\frac{-9 + 3}{2},\frac{7+5}{2})=(-3,6)$.

Step14: Solve for problem 22

For points $(1,3)$ and $(4,8)$, $x_1 = 1,x_2 = 4,y_1 = 3,y_2 = 8$. Then the mid - point is $(\frac{1+4}{2},\frac{3+8}{2})=(\frac{5}{2},\frac{11}{2})$.

Step15: Solve for problem 23

For points $(-6,7)$ and $(9,10)$, $x_1=-6,x_2 = 9,y_1 = 7,y_2 = 10$. Then the mid - point is $(\frac{-6 + 9}{2},\frac{7+10}{2})=(\frac{3}{2},\frac{17}{2})$.

Answer:

1. $(0,5)$
2. $(4,0)$
3. $(0,-3)$
4. $(-10,0)$
5. $(6,16)$
6. $(0,4)$
7. $(-2,-8)$
8. $(-3,-11)$
9. $(4,0)$
10. $(0,0)$
11. $(5,5)$
12. $(-3,6)$
13. $(\frac{5}{2},\frac{11}{2})$
14. $(\frac{3}{2},\frac{17}{2})$