## anonymous 4 years ago A(1,3) B(-3,5) find the perpendicular bisector equation

1. anonymous

i know the slope is -2

2. anonymous

Find the midpoint also, the perpendicular line will pass through this point.

3. anonymous

the midpoint is -1,4

4. anonymous

So can you write an equation for a line that passes through (-1,4) with a slope of 1/2?

5. anonymous

so it would be y-4 = 1 x-(-1) = 2 ?

6. anonymous

if slope is -2 of the original line given two vertices,therefor the slope of the perpendicular line is 1/2

7. anonymous

the answer is 2x - y = -6 but i get a different answer

8. ash2326

We have the line connecting the points A(1,3) and B(-3,5) the point which divides the line into two halves will have coordinates D(x1,y1) $x1= \frac{1+(-3)}{2}$ and $y1=\frac{3+5}{2}$ so we get $(x1,y1= (-2, 4)$ so the perpendicular bisector will pass through this point and we need one more condition like another point or slope to find out its equation here it's easy to find the slope of perependicular bisector Let the slope of AB be m1 and of the perpendicular bisector be m2 $m1= \frac{5-3}{-3-1}$ we get $m1= -\frac{1}{2}$ now since AB and its perpendicular bisector are perpendicular to each other $m1*m2=-1$ so $m2=2$ so we have the slope m2= 2 and the line passes through D(-2, 4) so equation will be $\frac{y-4}{x+2}= 2$ so we get $y-4=2x+2$ so the equation is $y-2x+6$

9. ash2326

$y-2x=6$

10. ash2326

or it can be written as $2x-y=-6$

11. anonymous

isnt the mid point (-1,4)?

12. anonymous

1 + (-3) = -2 then -2 / 2 = -1

13. anonymous

since the question is the perpendicular bisector equation of the line, we will be needing the midpoint and the perpendicular slope. .

14. ash2326

sorry I made a mistake then you'll get $\frac{y-4}{x+1}=2$ or $y-4=2x+2$ or $y-2x=6$ i made mistake 2 times and fortunately got the correct answer:)

15. anonymous

nikkyster if you got the slope to =2, you calculated the slope wrong

16. anonymous

The slope of the original line is -1/2

17. anonymous

i got the slope to be -2

18. ash2326

yeah slope of line is $-\frac{1}{2}$

19. anonymous

I should've double checked it earlier ;p

20. anonymous

But you have the right midpoint

21. anonymous

yeah your right ! i got the slope wrong

22. anonymous

what about for midpoint with a decimal?

23. anonymous

|dw:1328422479768:dw||dw:1328422542891:dw||dw:1328422687105:dw| therefor the perpendicular slope is 2, the equation of the perpendicular line is

24. anonymous

|dw:1328422920367:dw|

25. anonymous

A(3,1) B(-3,6)

26. anonymous

the midpoint is (0,3.5) and the slope would be -5/6

27. anonymous

is this another problem?

28. anonymous

yes

29. anonymous

what's the question? prependicular equation?

30. anonymous

perpendicular ?