## princesskks 3 years ago Write an equation for the locus of points equidistant from the lines y=3-3x and y=3x-3 .

1. benice

|dw:1332965903091:dw|

2. benice

first we need to find two point the same distance away from each equation

3. benice

so the first point can the intersection of the two line s y=3-3x y=3x-3 y=y 3-3x=3x-3 6x=6 x=1 therefore y =0 (0,1) we just need one more point and then we make an equation for that line

4. princesskks

ok so whats the next step to get the last point @benice

5. benice

ok so we could pick say y =6 for both lines y=3x-3 6=3x-3 3x=9 x=3 (3,6) y=3-3x 6=3-3x 3=-3x x=-1 (|dw:1332966561289:dw|-1,6)

6. benice

so in my poor drawing we have two points on the lines... you need to find the midpoint of the line to get your second point

7. princesskks

ok

8. princesskks

what is the formula to find the midpoint again @benice

9. benice

(x1+x2)/2 , (y1+y2)/2

10. princesskks

so do you multiply the amounts add subtract what ? @benice

11. benice

|dw:1332967284309:dw| for example

12. princesskks

so it would be (3+-1) /2 ,( 6+6) /2 ?

13. benice

yes

14. princesskks

and that is ( 1,6 ) the final answerr ? @benice ?

15. princesskks

and then what do you do after that to solve the problem ?

16. benice

remeber we need to find an equation that equal distance from both lines so we decide we would get two points (0,1) (1,6) now with these two points equal distance from both the lines this means they are on the line we are looking for so ,... how do the equation of the line with two points?

17. benice

sorry the points are (1,0) (1,6)

18. benice

|dw:1332967959443:dw|

19. princesskks

ok so now we have what we need to find the locus ? @benice

20. benice

yes find that line equation and your done

21. princesskks

ohh you see i didnt even know you responded back -__ - what is the formula for line equation ? @benice