## anonymous 5 years ago Can someone help me review the distance formula and how to calculate a midpoint?

1. anonymous

ok, sure...do you have any points to work with?

2. anonymous

Hold on and I'll get a few my teacher gave me to work with

3. anonymous

sure

4. anonymous

W(3, -12) M(2, -1)

5. anonymous

M is the midpoint

6. anonymous

ok, good start. so draw it on a graph first

7. anonymous

Ok one second

8. anonymous

you need to find the other point, let's call it P...

9. anonymous

Ok i have the graph drawn

10. anonymous

nice, so what is the midpoint formula?

11. anonymous

(X1+x2)/2 ; (Y1+y2)/ 2

12. anonymous

ok cool, so you have W:(3, -12), and you have the midpoint...so M=(2,-1)...right so use the formulas. let's look at (x1+x2)/2

13. anonymous

we have that $2 = (x1 + x2) / 2]\, and that x1 = the x-coordinate from W 14. anonymous x1 = 3, x2 = ? --> 2 = ( 3 + x2 )/2...solve for x2 15. anonymous what did you get? 16. anonymous this would be the x-coordinate for the point P we made up 17. anonymous I got -2 for X2 18. anonymous hey, you can refresh the page when it gets stuck ;) 19. anonymous ok.. I was freaking there for a sec 20. anonymous the x-coordinate for W is 3, so you say x2 = -2, let's put that back in the Midpoint equation for X: => so we have 3 from W and now we have -2 from x2 , this is (3 + -2) = 1, then 1/2 but the goal is 2 21. anonymous So this is how I got -2 for an answer 2=(3+X2)/2 -3 -3 (-1)=X2/2 x2 x2 -2= X2 22. anonymous so you should multiply both sides by 2 1. 2 = ( 3 + x2 ) /2 2. Multiply both sides by 2 (to get ride of the 2 on the right side) 2*2 = ( 3 + x2 ) /2 *2 = 4 = (3 +x2) 3. now we have [ 4 = (3 + x2) ], solve for x2 get x2 = 1 23. anonymous Oh... okay. I didn't know to do that. 24. anonymous you skipped ahead and subtracted 3 from both sides, but 3 is in the parantheses. it's like we can get the 3 because the whole thing ( 3 + x2 ) is being divided by 2, so the equation actually is 3/2 + x2/2 25. anonymous *can't get the 3... 26. anonymous you want to try the same process to find y? 27. anonymous Alright.. Thanks for telling me that, my math teacher thought it was okay not to tell us that. And if you want too. 28. anonymous yes, let's solve for the y-coordinate of P...we have P = ( x2, y2 ) --> P = ( 1, y2 ) 29. anonymous so you can look at your graph, and find 1 on the x-axis...now you're half way there to finding where P actually is 30. anonymous Okay 31. anonymous ok, so you're stuck at x=1, now you can only move up or down, changing y, so you have M on the graph and W on the graph, so you can make a guess at where P is just by checking out the graph... 32. anonymous Is it possible to use the slope intercept to find Y? or would that just add confusion? 33. anonymous you could, but you have a simple midpoint equation to find y... (y1 + y2) /2 = -1, with y1=-12, so ( -12 + y2 ) /2 = -1...solve it! 34. anonymous I ended up getting -14 35. anonymous what are your steps? remember that you have to multiply by 2 here before dealing with -12 36. anonymous (-12 + Y2)/2=-1 *2 *2 (-12 + y2)= -2 +-12 +-12 Y2= -14 37. anonymous ah, if you have -12 to both sides, you actually have (-24 + y2) = -14...so you should add 12 to both sides, to get y2 = -2 + 12 = 10 38. anonymous the goal was to get rid of -12 on the left side, but you can't just get rid of it, you have to keep the relationship that you already have....so if you get rid of -12 on the left side by adding 12 (thus getting 0), you have to do the same thing to the right side or else you've changed the relationship...it's all about find ways to reduce the problem 39. anonymous right, so what are the coordinates of our point P? 40. anonymous Okay, so the -2 we divided by is still on the right side of the equal sign? 41. anonymous right, you multiplied each side by 2 to get rid of the /2 on (y1 + y2), that would make the right side (-1) * (2) = -2 42. anonymous sorry, :(, I have to go, but I will be back in 15-20minutes 43. anonymous once you get the midpoint stuff down, you can work on the the distance formula, which is: \[d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 }$

44. anonymous

so, brb

45. anonymous

Okay I'll be here

46. anonymous

all right, are you finished with midpoint stuff?