80 !

a line segment has endpoints at (4, –6) and (0, 2). what is the slope of the given line segment? what is the midpoint of the given line segment? what is the slope of the perpendicular bisector of the given line segment? what is the equation, in slope-intercept form, of the perpendicular bisector?

1). Slope = (-2)

2). Midpoint = (2, -2)

3). Slope of the perpendicular bisector = (1/2)

4). Equation of perpendicular bisector will be x - 2y = 6

Step-by-step explanation:

A line segment has the endpoints at (4, -6) and (0, 2).

1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)

2). Mid point of the line segment is given by

Therefore midpoints of the line segment will be = (2, -2)

3). Slope of the perpendicular bisector is represented by

⇒ (-2)×m2 = (-1)

⇒

4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).

Since standard equation of the line will be given as y = mx + c

passes through (2, -2).

c = (-1) - 2 = -3

Finally the equation of perpendicular bisector will be

⇒ 2y = x - 6

⇒ 2y - x = -6

⇒ x - 2y = 6

6. 104

7. 52/37

8. 2704

9. 140608

10. -52

11. |52|=52

12. 1/52

13. 156

14. 26

15. 40

16. 37

17. -364

18. 53 1/3

19. 50.96

20. 43 2/3

21. 78

22. 50.75

23. 47.63

24. 163.28

25. 10400

26. 338

27. 208

28. 2704 square inches

29. 312 square meters

30. don't know what its asking, tell me so i can tell you

31. 8490.56

32. 52 degrees would be an acute angle

33. 128 degrees

34. 20.8

35. 39

36. 208