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)

Explanation:

19.

Step1: Recall mid - point formula

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

Step2: Calculate x - coordinate of mid - point

\(x=\frac{5 + 3}{2}=\frac{8}{2}=4\)

Step3: Calculate y - coordinate of mid - point

\(y=\frac{11+1}{2}=\frac{12}{2}=6\)

Step1: Apply mid - point formula

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

Step2: Compute x - coordinate

\(x=\frac{7 + 3}{2}=\frac{10}{2}=5\)

Step3: Compute y - coordinate

\(y=\frac{-5 + 3}{2}=\frac{-2}{2}=-1\)

Step1: Use mid - point formula

For \((x_1,y_1)=(-8,-11)\) and \((x_2,y_2)=(2,5)\), we have \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).

Step2: Find x - coordinate

\(x=\frac{-8+2}{2}=\frac{-6}{2}=-3\)

Step3: Find y - coordinate

\(y=\frac{-11 + 5}{2}=\frac{-6}{2}=-3\)

Answer:

\((4,6)\)

20.