Question

midpoint formula color by number
directions: find the midpoint of the line - segment with the given points. then, color the indicated coordinate (x or y) on the mandala with the color given. show your work on a separate sheet of paper.
line segment endpoints midpoint color

1. (6,4),(10, - 1) ____________ light blue (y)
2. (5, - 8),(3,4) ____________ dark blue (x)
3. (1, - 11),(1, - 8) ____________ maroon (y)
4. (-3,4),(-1, - 12) ____________ green (y)
5. (-1,7),(-1, - 8) ____________ yellow (x)
6. (-1,9),(5,9) ____________ black (y)
7. (-5, - 9),(-4,8) ____________ light blue (y)
8. (3, - 11),(-10,0) ____________ dark blue (x)
9. (4, - 10),(2,2) ____________ maroon (x)
10. (-6, - 7),(5, - 5) ____________ green (y)
11. (14,0),(-7,5) ____________ yellow (x)

given the midpoint and one endpoint of a line segment, find the other endpoint.

1. endpoint: (-9, - 1), midpoint: (8,14) ____________ black (x)
2. endpoint: (10,12), midpoint: (6,9) ____________ light blue (x)
3. endpoint: (-8, - 10), midpoint: (10, - 7) ____________ maroon (x)

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 problem 1

For points $(6,4)$ and $(10, - 1)$:
$x=\frac{6 + 10}{2}=\frac{16}{2}=8$
$y=\frac{4+( - 1)}{2}=\frac{3}{2}=1.5$
The mid - point is $(8,1.5)$

Step3: Solve problem 2

For points $(5, - 8)$ and $(3,4)$:
$x=\frac{5 + 3}{2}=\frac{8}{2}=4$
$y=\frac{-8 + 4}{2}=\frac{-4}{2}=-2$
The mid - point is $(4,-2)$

Step4: Solve problem 3

For points $(1,-11)$ and $(1,-8)$:
$x=\frac{1 + 1}{2}=1$
$y=\frac{-11+( - 8)}{2}=\frac{-19}{2}=-9.5$
The mid - point is $(1,-9.5)$

Step5: Solve problem 4

For points $(-3,4)$ and $(-1,-12)$:
$x=\frac{-3+( - 1)}{2}=\frac{-4}{2}=-2$
$y=\frac{4+( - 12)}{2}=\frac{-8}{2}=-4$
The mid - point is $(-2,-4)$

Step6: Solve problem 5

For points $(-1,7)$ and $(-1,-8)$:
$x=\frac{-1+( - 1)}{2}=\frac{-2}{2}=-1$
$y=\frac{7+( - 8)}{2}=\frac{-1}{2}=-0.5$
The mid - point is $(-1,-0.5)$

Step7: Solve problem 6

For points $(-1,9)$ and $(5,9)$:
$x=\frac{-1 + 5}{2}=\frac{4}{2}=2$
$y=\frac{9 + 9}{2}=\frac{18}{2}=9$
The mid - point is $(2,9)$

Step8: Solve problem 7

For points $(-5,-9)$ and $(-4,8)$:
$x=\frac{-5+( - 4)}{2}=\frac{-9}{2}=-4.5$
$y=\frac{-9 + 8}{2}=\frac{-1}{2}=-0.5$
The mid - point is $(-4.5,-0.5)$

Step9: Solve problem 8

For points $(3,-11)$ and $(-10,0)$:
$x=\frac{3+( - 10)}{2}=\frac{-7}{2}=-3.5$
$y=\frac{-11 + 0}{2}=\frac{-11}{2}=-5.5$
The mid - point is $(-3.5,-5.5)$

Step10: Solve problem 9

For points $(4,-10)$ and $(2,2)$:
$x=\frac{4 + 2}{2}=3$
$y=\frac{-10 + 2}{2}=\frac{-8}{2}=-4$
The mid - point is $(3,-4)$

Step11: Solve problem 10

For points $(-6,-7)$ and $(5,-5)$:
$x=\frac{-6 + 5}{2}=-\frac{1}{2}=-0.5$
$y=\frac{-7+( - 5)}{2}=\frac{-12}{2}=-6$
The mid - point is $(-0.5,-6)$

Step12: Solve problem 11

For points $(14,0)$ and $(-7,5)$:
$x=\frac{14+( - 7)}{2}=\frac{7}{2}=3.5$
$y=\frac{0 + 5}{2}=2.5$
The mid - point is $(3.5,2.5)$

Step13: Solve problem 12

Let the other endpoint be $(x,y)$.
We know that $\frac{-9 + x}{2}=8$ and $\frac{-1 + y}{2}=14$
For $x$: $-9+x = 16$, so $x=16 + 9=25$
For $y$: $-1+y = 28$, so $y=28 + 1=29$
The other endpoint is $(25,29)$

Step14: Solve problem 13

Let the other endpoint be $(x,y)$.
We know that $\frac{10 + x}{2}=6$ and $\frac{12 + y}{2}=9$
For $x$: $10+x = 12$, so $x=12 - 10=2$
For $y$: $12+y = 18$, so $y=18 - 12=6$
The other endpoint is $(2,6)$

Step15: Solve problem 14

Let the other endpoint be $(x,y)$.
We know that $\frac{-8 + x}{2}=10$ and $\frac{-10 + y}{2}=-7$
For $x$: $-8+x = 20$, so $x=20 + 8=28$
For $y$: $-10+y=-14$, so $y=-14 + 10=-4$
The other endpoint is $(28,-4)$

Answer:

1. $(8,1.5)$
2. $(4,-2)$
3. $(1,-9.5)$
4. $(-2,-4)$
5. $(-1,-0.5)$
6. $(2,9)$
7. $(-4.5,-0.5)$
8. $(-3.5,-5.5)$
9. $(3,-4)$
10. $(-0.5,-6)$
11. $(3.5,2.5)$
12. $(25,29)$
13. $(2,6)$
14. $(28,-4)$