Question

example 3
find the coordinates of the midpoint of a segment with the given endpoints.

1. (5, 11), (3, 1)
2. (7, - 5), (3, 3)
3. (-8, -11), (2, 5)
4. (7, 0), (2, 4)
5. (-5, 1), (2, 6)
6. (-4, -7), (12, -6)
7. (2, 8), (8, 0)
8. (9, -3), (5, 1)
9. (22, 4), (15, 7)
10. (12, 2), (7, 9)
11. (-15, 4), (2, -10)
12. (-2, 5), (3, -17)
13. (2.4, 14), (6, 6.8)
14. (-11.2, -3.4), (-5.6, -7.8)

example 4
find the coordinates of the missing endpoint if b is the midpoint of $overline{ac}$.

1. c(-5, 4), b(-2, 5)
2. a(1, 7), b(-3, 1)
3. a(-4, 2), b(6, -1)
4. c(-6, -2), b(-3, -5)
5. a(4, -0.25), b(-4, 6.5)
6. c($\frac{5}{3}$, -6), b($\frac{8}{3}$, 4)

examples 5 and 6
suppose m is the midpoint of $overline{fg}$. find each missing measure.

1. fm = 5y + 13, mg = 5 - 3y, fg =?
2. fm = 3x - 4, mg = 5x - 26, fg =?
3. fm = 8a + 1, fg = 42, a =?
4. mg = 7x - 15, fg = 33, x =?
5. fm = 3n + 1, mg = 6 - 2n, fg =?
6. fm = 12x - 4, mg = 5x + 10, fg =?
7. fm = 2k - 5, fg = 18, k =?
8. fg = 14a + 1, fm = 14.5, a =?
9. mg = 13x + 1, fg = 15, x =?
10. fg = 11x - 15.6, mg = 10.9, x =?

mixed exercises
find the coordinates of the missing endpoint if p is the midpoint of $overline{nq}$.

1. n(2, 0), p(5, 2)
2. n(5, 4), p(6, 3)
3. q(3, 9), p(-1, 5)

Explanation:

19.

Step1: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1 = 5,y_1=11,x_2 = 3,y_2 = 1\).
\[x=\frac{5 + 3}{2},y=\frac{11+1}{2}\]

Step2: Calculate \(x\) and \(y\) values

\[x=\frac{8}{2}=4,y=\frac{12}{2}=6\]

Step1: Apply mid - point formula

For points \((x_1,y_1)=(7, - 5)\) and \((x_2,y_2)=(3,3)\), use \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
\[x=\frac{7 + 3}{2},y=\frac{-5 + 3}{2}\]

Step2: Compute coordinates

\[x=\frac{10}{2}=5,y=\frac{-2}{2}=-1\]

Step1: Use mid - point formula

Given \((x_1,y_1)=(-8,-11)\) and \((x_2,y_2)=(2,5)\), we have \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
\[x=\frac{-8 + 2}{2},y=\frac{-11 + 5}{2}\]

Step2: Calculate the mid - point

\[x=\frac{-6}{2}=-3,y=\frac{-6}{2}=-3\]

Answer:

\((4,6)\)

20.