Question

Find the midpoint of each segment in Exercise 1 above.Example: The midpoint M between point E and point F is calculatedwith the Midpoint Formula.

Answer 1

We have to calculate the midpoint for each segment.

To do that we have to calculate the average for the coordinates of each point.

1) For AB, we have A = (-5,8) and B = (-5,6).

We can then calculate the midpoint coordinates as:

`M_(AB)=((x_A+x_B)/(2),(y_A+y_B)/(2))=((-5+(-5))/(2),(8+6)/(2))=(-(10)/(2),(14)/(2))=(-5,7)`

2) For BC we have B = (-5,6) and C = (-2,6).

The midpoint will be:

`M_(BC)=((-5+(-2))/(2),(6+6)/(2))=((-7)/(2),(12)/(2))=(-(7)/(2),6)`

3) For CD we have C = (-2,6) and D = (2,3).

The midpoint will be:

`M_(CD)=((-2+2)/(2),(6+3)/(2))=((0)/(2),(9)/(2))=(0,(9)/(2))`

4) For DE we have D = (2,3) and E = (2,-1).

The midpoint will be:

`M_(DE)=((2+2)/(2),(3+(-1))/(2))=((4)/(2),(2)/(2))=(2,1)`

5) For EF we have E = (2,-1) and F = (6,0).

The midpoint will be:

`M_(EF)=((2+6)/(2),(-1+0)/(2))=((8)/(2),-(1)/(2))=(4,-(1)/(2))`

Answer:

AB = (-5,7)

BC = (-7/2,6)

CD = (0,9/2)

DE = (2,1)

EF = (4,-1/2)